School of Engineering Sciences Faculty of Mechanical Science and Engineering Institute of Materials Science, Chair of Material Science and Nanotechnology Modeling and simulation of photocatalytic degradation of organic components in wastewater Hagen Eckert Born on: 28.03.1988 in Greifswald Dissertation to achieve the academic degree Doktoringenieur (Dr.-Ing.) Referees Prof. Dr. Gianaurelio Cuniberti Prof. Dr. Cormac H. Toher Prof. Dr. Hans-Peter Wiesmann Submitted on: 06.08.2020 Defended on: 15.12.2020
Transcript
School of Engineering Sciences Faculty of Mechanical Science and Engineering
Institute of Materials Science, Chair of Material Science and Nanotechnology
Modeling and simulation ofphotocatalytic degradation oforganic components inwastewaterHagen EckertBorn on: 28.03.1988 in Greifswald
Dissertationto achieve the academic degree
Doktoringenieur (Dr.-Ing.)
Referees
Prof. Dr. Gianaurelio CunibertiProf. Dr. Cormac H. ToherProf. Dr. Hans-Peter Wiesmann
Submitted on: 06.08.2020
Defended on: 15.12.2020
Statement of authorship
I hereby certify that I have authored this Dissertation entitled Modeling and simula-tion of photocatalytic degradation of organic components in wastewater independentlyand without undue assistance from third parties. No other than the resources and
references indicated in this thesis have been used. I have marked both literal and ac-
cordingly adopted quotations as such. There were no additional persons involved in
the intellectual preparation of the present thesis. I am aware that violations of this
declaration may lead to subsequent withdrawal of the degree.
Dresden, 06.08.2020
Hagen Eckert
EST AD ASTRA MOLLIS E TERRIS VIA - Seneca
Acknowledgment
During my time at the TU Dresden, I had the pleasure of meeting a wonderful group
of people. The thesis as it stands now would not have been possible without them.
Foremost, I would like to thank Prof. Cuniberti for providing me the opportunity to
explore the numerous facets of computational material science. His guidance and
support throughout the years helped me to become a better scientist. Through his re-
lentless work, I was able to learn in a well-equipped research environment with brilliant
colleagues from all over the world.
I would like to thank Prof. Toher and Prof. Wiesmann for their interest in my research
and willingness to review this thesis.
Many people provided me with advice and took time out of their days to discuss my
questions and ideas. While not all of them can be mentioned by name, I would like to
point out Alexander, Arezoo, Rafael, Annegret, and Giovanni. I have to especially em-
phasize Manfred for helping me to keep my focus, and for his sound scientific inputs. I
would like to express my gratitude towards Manuela, Grit, and Sylvi, for being the back-
bone of our research. Without you, we would have gotten lost in the administrative
jungle long ago. While I took some detours, Sara, Nga, and Thomas provided me the
motivation to follow suit. I am thankful not just for the pleasant time we spent at work
but also for their friendships.
A crucial aspect of my time as PhD student was the opportunity to visit outstanding
research groups around the world. I would like to express my thanks to Prof. Clementi,
Prof. Persson, Prof. Pasquali, Prof. Lanceros-Mendez, and Prof. Shirai for being excel-
lent hosts. Here I also thank Scott and James, my roommates of choice, to guiding me
through the urban wilderness of Houston.
While research can be challenging at times, my friends and family kept me sane. Thank
you all for the big and small adventures we concluded and for the ones yet to come. I
have to formally apologize to Anna, Julia, Oliver, Philipp, Robert, and Sophia for making
them proofread parts of this thesis or to be beta-testers. Your sacrifices are much
appreciated. Numerous people accompany me on my path to this point in life. While
I sadly have to admit that I lost touch with some, all of them had an impact on me.
Organic pollutants are discharged into the water cycle at many stages in our daily
lives. Conventional wastewater treatments are ineffective in the removal of some
of them, especially clearing pharmaceuticals. Photocatalytic degradation utilizing cat-
alytic nanosuspensions under ultraviolet irradiation represents an efficient method
to reduce those organic components in the wastewater. While the general concept
of photocatalytic water purification is well established, a descriptive and easy to use
model of the essential processes was missing. Such a model is critical to ensure the
systematic comparability of experimental results and supports process optimization.
This work presents a modeling approach to simulate the involved kinetic processes
based on the Langmuir–Hinshelwood mechanism. Further, the fundamental model
is extended to include the formation of intermediate organic components. This ex-
tension uses either an incremental degradation mechanism or a fragmentation based
mechanism, that can include excess bonds. The simulated concentration evolution of
intermediates, as well as the evolution of the total organic carbon, are discussed for dif-
ferent model assumptions concerning their desorption rates from the photocatalyst
surface. The model parameters were estimated from comparison with experimental
findings. Basic experiments were performed using the antibiotic ciprofloxacin, and
the dye methylene blue as organic compounds and titanium dioxid and zinc oxide as
photocatalytic materials. Furthermore, the application of the model to more complex
systems is shown by the photocatalytic degradation of 14 pharmaceuticals in wastew-
ater treatment plant effluent. Following successful evaluation of this model, it was
implemented in an open-source software package to enable a wider adoption and a
sound foundation for further developments.
8
Kurzfassung
Organische Schadstoffe werden in vielen Phasen unseres täglichen Lebens in den
Wasserkreislauf eingeleitet. Die herkömmliche Abwasserbehandlung ist nicht zur ef-
fektiven Entfernung einiger dieser Stoffe, insbesondere von Arzneimitteln, geeignet.
Die Fotokatalyse basierend auf der Suspension von katalytischen Nanopartikeln und
ultraviolettem Licht stellt eine effiziente Methode dar, um diese organischen Stoffe
im Abwasser zu reduzieren. Während das allgemeine Konzept der fotokatalytischen
Wasserreinigung gut etabliert ist, fehlte ein beschreibendes und einfach anwendbares
Modell der wesentlichen Abbauprozesse. Ein solches Modell ist entscheidend, um ex-
perimentelle Ergebnisse systematisch vergleichen zu können, und stellt eine wertvolle
Hilfe bei der Optimierung von Prozessen dar. Diese Arbeit präsentiert einen Model-
lierungsansatz zur Simulation der kinetischen Prozesse basierend auf dem Langmuir-
Hinshelwood-Mechanismus. Dieses Grundmodell wurde erweitert, um auch die Bil-
dung von organischen Zwischenprodukten zu beschreiben. Diese Erweiterungen ba-
sieren entweder auf einem inkrementellen oder einen fragmentierenden Abbaume-
chanismus, der durch das Einbinden von überschüssigen Bindungen ergänzt werden
kann. Die simulierte Konzentrationsentwicklung von Zwischenprodukten sowie die Ent-
wicklung des verbleibenden organischen Kohlenstoffes werden für verschiedene Mo-
dellannahmen bezüglich ihrer Desorptionsraten von der Photokatalysatoroberfläche
diskutiert. Die Modellparameter wurden aus dem Vergleich mit experimentellen Er-
gebnissen ermittelt. Grundlegende Experimente wurden unter Verwendung des Anti-
biotikums Ciprofloxacin und des Farbstoffs Methylenblau als Beispiele für organische
Verbindungen und Titandioxid und Zinkoxid als fotokatalytische Materialien durchge-
führt. Darüber hinaus wird die Anwendbarkeit des Modells auf komplexere Systeme
durch den Vergleich mit dem fotokatalytischen Abbau von 14 Medikamenten im Ab-
fluss von Kläranlagen demonstriert. Nach der Evaluierung des Modells wurde es in ein
Open-Source-Softwarepaket implementiert, um eine breitere Anwendung zu ermögli-
chen und eine solide Grundlage für weitergehende Entwicklungen zu schaffen.
9
Symbols
Some symbols that are not central to this thesis are not listed in the following table,
but instead directly explained in the text near to their occurrence. Numbers in curly
brackets refer to chemical reactions.
Symbol Description Definition
α absorption coefficient 2.8
β excess bond split 3.40
δp penetration depth 2.13
ε molar extinction coefficient 3.6
εe energy state
η viscosity
κ adsorption prefactor (m) 3.29
μp hole mobility
ν photon frequency
ν0 pre-exponential factor (s−1) 3.29
φ quantum yield
Φ effective quantum yield 2.17
τp hole life-time
Θ surface coverage 3.14
A absorbance 3.6
as specific surface area (m−1) 3.9
Am surface area covered per molecule (m2) 3.14
A(ad) adsorbed organic molecule {8}
A(aq) organic molecule in solution {8}
b excess bond count {11}
CA(ad),0 initial concentration of adsorbed organic molecules (m−2)
CA(ad) concentration of adsorbed organic molecules (m2)
CA(aq),0 initial concentration of organic molecules in solution (m−3)
CA(aq) concentration of organic molecules in solution (m)
CA(ad),∞ equilibrium concentration of adsorbed organic molecules (m−2) 3.20
CA(aq),∞ equilibrium concentration of organic molecules in solution (m−3) 3.20
CBET BET parameter 3.1
10
Symbol Description Definition
COx concentration oxidizing species
CRed concentration reduction species
D diffusion coefficient
E excess bond {11}
EF Fermi level
Ebend potential difference band bend
Edes desorption energy (J) 3.29
EF,redox redox fermi level 2.5
Eg bandgap energy
FF Fermi function 2.1
FK,M Kubelka-Munk remission function 3.5
I transmitted intensity 3.6
I0 photon flux (m−2 s−1)
Ii incident intensity 3.6
jads adsorption flux (m−2 s−1)
jdes desorption flux (m−2 s−1)
jph photocurrent density
jreac reaction flux (m−2 s−1)
K absorption coefficient 3.2
kads adsorption rate constant (m s−1) 3.11
kapp apparent rate constant (s−1) 3.22
kdes desorption rate constant (s−1) 3.11
kreac reaction rate constant (s−1) 3.11
Lp hole diffusion length 2.15
M(aq) mineralized components {8}
n molecule size index
Ns density of donor/acceptor states
NA molecule count organic species
na specific amount adsorbed (mol g−1) 3.1
nm specific monolayer amount of adsorbate (mol g−1) 3.1
p pressure of the adsorptive in equilibrium with the adsorbate (Pa) 3.1
p0 saturation vapour pressure of the adsorptive (Pa) 3.1
11
Symbol Description Definition
R reflectance 3.4
S scattering coefficient 3.2
T temperature
TL light transmittance 3.6
U potential 2.3
U◦ standard potential
U◦redox
standard reduction potential
V volume
Wdl depletion layer width 2.14
z number of electrons
Constants
This work uses CODATA1 recommended values for fundamental physical constants [1].
The table below lists the values for the ones used.
Symbol Description Value
ε0 electric constant 8.854188 • 10−12 Fm−1
e elementary charge 1.602177 • 10−19 C
F Faraday constant 9.648533 • 104 Cmol−1
h Planck constant 6.626070 • 10−34 J s
kB Boltzmann constant 8.617330 • 10−5 eVK−1
NAvo Avogadro constant 6.022141 • 1023 mol−1
R molar gas constant 8.314460 J(mol K)−1
1Committee on Data for Science and Technology of the International Science Council
12
Abbreviations
Abbreviation Description
AOP advanced oxidation processes
BET Brunauer-Emmett-Teller method
CB conduction band
HPLC high-performance liquid chromatography
IUPAC International Union of Pure and Applied Chemistry
LED Light-emitting diodes
LH Langmuir-Hinshelwood
LLoQ lower limit of quantification
LSODE Livermore Solver for Ordinary Differential Equations
MS/MS tandem mass spectrometry
NPOC non-purgable organic carbon
OLED organic light-emitting diodes
RHS right-hand side
SEM scanning electron microscope
SPE solid-phase extraction
TOC total organic carbon
UV ultraviolet
VB valence band
WWTP wastewater treatment plant
13
1. Motivation
Many pollutants, such as heavy metals, dyes, and pharmaceuticals, are discharged
into the water cycle at many stages in our daily lives. Pharmaceuticals are mostly in-
troduced in the sewage system through excretion of unmetabolized compounds af-
ter medical use or inappropriate disposal [2, 3, 4, 5], and reach the local wastewater
treatment plants (WWTPs). However, conventional WWTPs are not designed to treat
water that is polluted with trace levels of various pharmaceuticals. The conventionally
applied treatments are ineffective in their removal, in particular, due to interactions
of the biological cleaning stages with the pharmaceuticals [6, 7]. Consequently, they
reach the aquatic system and can be found in the surface and groundwater [8, 9], soil
and sediments [9, 10], and even in drinking [11, 12] and tap water [9, 13]. Commonly,
extreme diluted medicinal drugs, in the range of ng to µg per liter, do not present
acute toxic effects on aquatic organisms. Nevertheless, concerns have been raised
for chronic exposure, due to their continuous input into the environment, acting as
slightly persistent pollutants [3, 5, 14]. This problem is amplified through the high level
of pharmaceuticals that are used nowadays. The median non-hospital pharmaceuti-
cal consumption per capita in 2008 for high-income countries was 1042 SU2 [15]. This
subscription volume was a growth of over 18% compared to the year 2000. In par-
ticular, antibiotics represent a severe problem because of their toxicity to microflora
and -fauna, and of the possible development of antibiotic-resistant microorganisms
[16, 17, 18]. Global over- and misuse of antibiotics has intensified that problem and
resulted in steadily increasing concentrations in wastewater [19]. With nearly eight-
times higher consumption compared to low-income countries, rich countries need to
intensify their efforts to lower the over- and misuse of pharmaceuticals products and
2“One IMS Standard Unit equals one tablet, one capsule, one suppository or pessary, one pre-filled
syringe/cartridge, pen, vial or ampule, one dose of an inhaled medicine or 5mL of an oral syrup or
suspension.” [15]
15
1. Motivationto lessen their effect on the environment.
In parts of the world with an intensive clothing industry (like China, Bangladesh, Viet
Nam, India, Turkey [20]), the attention is more frequently placed on dyes entering the
water cycle. Some dyes are toxic, mutagenic [21], or carcinogenic [22]. Therefore, the
removal of dyes from the wastewater is imperative. While the number of different
chemicals used in the dye industry is indeed small compared to pharmaceuticals, the
range of different substances is still extensive. In the European REACH3 database [23]
in the product category “Textile dyes, and impregnating products” (November 2018)
over 2150 chemicals were registered. While the overall production of around 900 thou-
sand tonnes of organic dyes in the year 2003, [24] is low compared to other chemical
substances, the amount that can be found in the environment is still significant. The
high volumes of water required during some dyeing processes inflate the amount of
produced waste drastically. In 1977 Anliker published a review titled “Color chemistry
and the environment,” where he stated from personal experience that around 10 -
20% of the active dyes are lost in the residual liquid waste [25]. Even though this re-
view was published more than 40 years ago, it is reasonable to assume that the order
of magnitude still applies for parts of the textile industry. In particular, in less devel-
oped countries outdated but low-cost production facilities are often still in use and
lead to high pollution levels in the clothing industry to this day.
Diverse efforts have been made to remove organic molecules from wastewater, such
as membrane filtration, activated carbon adsorption, and advanced oxidation pro-
cesses (AOP). AOPs are advantageous when the pollutants have a high chemical sta-
bility. Almost the total mineralization of contaminants to carbon dioxide, water, and
inorganic compounds can be achieved. If this is not the case, a partial oxidation can,
at least, help to make the initial pollutants more biodegradable [4, 26]. Different tech-
niques involve the generation of hydroxyl radicals, which are non-selective and have
twice the oxidizing power of chlorine [5, 7, 27, 28, 29]. The non-selectiveness is essen-
tial when dealing with such diverse pollutants as pharmaceuticals or dyes. Heteroge-
neous semiconductor photocatalysis has become an attractive method to remediate
environmental contamination due to its high photocatalytic activity, non-toxicity, and
photostability [4, 27, 30, 31, 32, 33]. Successful degradation experiments have been
reported [34] for various organic molecules, such as azo dyes [35], furfural [36], sul-
famethoxazole [37], and acetylene [31].
Understanding andmodeling the processes related to the degradation of organic mol-
3Registration, Evaluation, Authorisation, and Restriction of Chemicals
16
ecules are essential for the development and characterization of new materials and
methods. This idea forms the core of this thesis. To establish a descriptivemodel, a set
of experimental systems is used as its foundation. These experiments are based on a
slurry mixture of photocatalytic nanoparticles to maximize the surface area of the sys-
tem. The up-scaling of such a setup can provide challenges regarding the separation
of the nanoparticles from the water after the treatment. As exemplary photocatalysts,
titaniumdioxide (TiO2), and zinc oxide (ZnO) were chosen and compared in their degra-
dation efficiencies. Even though several semiconductors have been studied for appli-
cations in wastewater decontamination, ZnO and TiO2 are frequently themost studied
photocatalysts because of their interesting optical properties, low cost, and availability
[38]. Although ZnO is usually described as the most active semiconductor [39], TiO2
is used more frequently because it is more stable than ZnO in aqueous solution [40].
Whenever photocatalytic systems are applied in an actual wastewater treatment plant,
a risk assessment regarding thematerial output into the environment is necessary due
to their photoactivity, size distribution, and potential toxicity for aquatic organisms in
the case of ZnO [41]. While such a study is out of the scope of this work, the properties
and risks of the used materials are discussed in more detail in Sec. 2.3 (p. 31).
The simulation of the kinetic processes, which are involved in the photocatalytic oxida-
tion of organic pollutants, are expected to lead to a deeper quantitative understanding
of the whole mineralization process. This understanding could help in optimizing the
design of reactors for photocatalytic water purification. A further issue of reactor de-
sign is the radiation transport in the reaction volume, investigated for example, in [42,
43, 44]. The degradation kinetics of organic pollutants has often been described within
the framework of the Langmuir-Hinshelwood (LH) model (see e.g., [45] and references
therein). For example, Minero [46] discussed several kinetic models of the photocat-
alytic process with the aim to obtain equations with physical meaning and reduced
complexity. Experimental validation of reported kinetic models has been performed
by Andreozzi et al. [47] for the photocatalytic degradation of 4-nitrophenol. The LH
model, combined with a Lambert-Beer type model for radiation transport, has been
applied to describe the degradation of methylene blue by Sannino et al. [48].
Generally, the photocatalytic mineralization of organic molecules is a complex process,
where parts of the initial molecules are oxidized step by step on the catalyst surface in
the presence of photo-generated radicals. These radicals can destroy the molecules’
bonds, thereby breaking them into smaller molecules. These molecules may then des-
orb from the surface of the photocatalyst. Consequently, various intermediate mol-
17
1. Motivationecules of different sizes emerge in the solution. In this work, three advanced model
approaches of photocatalytic degradation are presented. These models extend the
single-species approach [45, 48, 49] by including the evolution of intermediates. In a
first case, the degradation by successive oxidation of the elements of the initial mole-
cules, excluding the possibility of molecule fragmentation, is studied. Within a second
complementary model, random fragmentation of organic molecules into smaller inter-
mediates and oxidation of the smallest fragments is considered. The last model aims
to correct the interpretation of the organic molecule as a simple chain through the
inclusion of excess bonds.
18
2. Introduction
2.1. Modeling and simulation
Simulation in materials science aims to determine, understand, and predict the prop-
erties of actual materials. In the initial phase of computerized research, only simple
models could be evaluated. They often just described pure crystalline materials or ba-
sic reaction correlations. In the meantime, a large number of models are available and
deployable on increasingly powerful computational resources. Nowadays, it is possi-
ble to enhance research in a wide range of materials science topics with the aid of
simulation.
The creation of models is necessary independently of computer simulations, since it is
difficult to gain direct knowledge even in a clearly defined system. This predicament is
rooted in the problem that the monitored systems and their interactions cannot be in-
vestigated adequately or not directly in nearly all cases. For this reason, an abstraction
step is essential for the scientific process. The simple imitation of real relationships to
gain knowledge can be seen as the origin of modeling. The structures of a real system
are thereby reproduced in a similar but simplified way - a model.
For example, experiments can be interpreted as a particular form of modeling. In an
experiment, the challenge lies in translating the experiment setup into models and
back again. Without a clear abstraction layer, it would not be possible to generate
reliable and comparable data from experiments. In theoretical modeling, the primary
focus is more on changing the degree of abstraction. This evolution from elementary
models to complex systems to describe a given system better and better over time can
frequently be observed in science. Thus, constant efforts to describe our surrounding
19
2. Introductionworld in more detail helped to understand it on new levels.
With the development of computer technology, increasingly sophisticated models of
real systems have become feasible. Old ideas to describe certain scientific aspects can
nowadays be used, due to the massive increase in computational power.
For example, Deep Learning is a topic that receives a tremendous amount of attentionin many areas of our daily and scientific life. The gross of the theoretical groundwork
was already completed in 1986 in work presented by Rumelhart, Hinton, and Williams
on convolutional neural networks [50]. However, it took over 25 years before the the-
oretical found methods would be used on the wide-scale we see today. Besides the
growth in processing power, additions to the initial ideas played a critical role as well.
Scientists were long fascinated with the idea to describe the behavior of atoms and
molecules withmathematical rules. One of themethods to describe these interactions
are molecular dynamics simulations, which are already conducted since the 1950s. In
this field, the growth of computational power can be very impressively demonstrated
by the systems that are investigated. Alder and Wainwright showed in their 1959 pub-
lication [51] experiments with 32 to 108 particles but claimed already that ‘Computers
now being planned should be able to handle ten thousand molecules in calculations
which do not require very many collisions.’ With the development of better force field
descriptions (Lennard-Jones potential) andmore robust computational systems, more
realistic systems could be tackled. So could Rahman calculate a good approximation
for self-diffusion of Argon in 1964 [52]. Roughly ten years later, in 1975, the first suc-
cessful folding of a protein was published by Levitt and Warshel [53]. The addition of
watermolecules as solvents was possible around 1988 to describe the behavior of pro-
teins more reliable [54]. Another critical dimension that developed was the length of
the time axis that could be explored. Duan and Kollman were able to observe protein
folding in water for 1µs instead of the 200ps ten years prior [55]. A very impressive
milestonewas themodeling of the Satellite TobaccoMosaic Viruswith up to 1,068millionatoms in 2006 by Freddolino et al. [56].
Nowadays, it is possible to create a virtual system in the rough likeness of a real sys-
tem. As symbolically show in Fig. 2.1, all three pillars of modern science: (i) theory, (ii)
experiment, and (iii) simulation are part of the overall process. In a traditional setup,
just the left half in this representation (theory and experiment) would be used. A the-
ory would be created to describe a system, and a loop of observing and manipulating
the real system would generate data to bring the theory to a descriptive model. A
20
2.1. Modeling and simulation
Model
Theory Experiment Simulation
SystemReal Virtual
System
abstract
constrain
create
observe
parameterize
obser
ve
initialize
manipulate
manipulate
Figure 2.1.: Relationship between the model and the real and virtual systems.
virtual system can now be created by simulating the model. The boundaries and con-
straints of the new systems are mostly derived from the initial theory-crafting process.
The experimental observations generate initial values and properties. After the model
is parameterized and prepared for the simulation, observations can be made. The
observation manipulation loop is much faster and easier to drive compared to the
experimental loop. This tight loop is one of the main advantages of using a virtual
system.
For a long time, computational simulations were just used to confirm experimental
findings or to interpret them. In these cases, the model is already established and
often well examined by experiments. With the higher level of available computational
power, simulations can cover vast parameter spaces while running the manipulation /
observation loop. This extension opens the option to start with just a few or without
experimental data at all. A constant reiteration of the model based on the received re-
sults is often implemented. The virtual system in such an instance can be used to pre-
dict the outcome of experiments in the real world. Especially for very time-consuming
experiments, this method can be used as a powerful tool to preselect promising candi-
dates. It is important to note that the results of a virtual system without experimental
verification should always be treated with caution.
The goal often seems to be the perfect model. Here it must be noted that someone
21
2. Introductionwhowould be able to create such a perfectmodel of a systemwould, in fact, not need it.
This person could directly understand the original in its whole complexity. Especially in
materials science, wheremanymechanisms on different sizes and time scales interact,
a single monolithically approach is not likely to be successful. Often individual models
have to be cross-linked to obtain application-relevant information. In this work, too, the
overall picture of the system is created by combining different methods on different
scales to obtain a better understanding of the examined system.
2.2. Heterogeneous photocatalysis
2.2.1. History
The influence of light on our environment is a topic that is connected with humankind
for eons. Chemical reactions that were driven by light were first discovered around
1790 by Joseph Priestley (1733-1800). His experiments with nitric acid can be seen as
the start of modern photochemistry [57].
The interest in catalytic photoreactions started in the 1900s. An example is the oxida-
tion of oxalic acid to formic acid with uranyl as catalytic material in 1911 by Bruner and
Kozak [58]. Even with their research limited to sunny spring and summer days, they
could already establish many essential connections like between the reaction rate and
the light intensity or the higher efficiency of blue/violet light. The word photocatalysis
was often used in the beginning 1900s to describe photosynthesis [59, 60]. This kind
of reactions would not be counted to the photocatalysis definition nowadays. The
International Union of Pure and Applied Chemistry (IUPAC) [61] defines the term pho-
tocatalysis as:
“Change in the rate of a chemical reaction or its initiation under the action
of ultraviolet, visible, or infrared radiation in the presence of a substance
—the photocatalyst— that absorbs light and is involved in the chemical
transformation of the reaction partners.”
and photocatalyst accordingly:
“Substance able to produce, by absorption of ultraviolet, visible, or infrared
radiation, chemical transformations of the reaction partners, repeatedly
22
2.2. Heterogeneous photocatalysiscoming with them into intermediate chemical interactions and regenerat-
ing its chemical composition after each cycle of such interactions.”
In the modern interpretation, heterogeneous photocatalysts are often semiconduc-
tors. First, mainly bulk semiconductors systems were studied to understand the sur-
face properties and reactions under visible irradiation. The area did not see much
activity due to problems with long-term stability and high cost. A new spark was cre-
ated with the now exceptionally highly cited Nature paper by Fujishima and Honda in
1972 [62]. In this publication, they describe the use of TiO2 to split water. A further
accelerator was the first oil crisis in 1973. During this time, the over-dependence on
fossil fuel got apparent, and the possibility to create fuel through water splitting from
light was encouraging. It was evident early on to the scientist in this field that using
light to foster chemical reactions will be an essential part of creating a sustainable fu-
ture. Already in 1912, Giacomo Ciamician stated in his New York speech about the
Photochemistry of the Future [63]:
“So far, human civilization has made use almost exclusively of fossil solar
energy. Would it not be advantageous to make better use of radiant en-
ergy?”
However, the first iterations based on the findings of Fujishima and Honda still battled
with problems in long-term stability and efficiency. Intertwining of nanotechnology in
the field during the last decades helped to overcome some of the downfalls. Nanos-
tructured photocatalysts are now the most promising pathway. In this section, the
physical and chemical properties of the bulk semiconductor and the critical effects of
the nanostructure are discussed.
2.2.2. Semiconductor band structure
A more in-depth look into the electron structure of the explored semiconductors is
necessary to approach the process of photocatalysis. In a commonly used depiction,
the electron structure is described by bands of allowed energy levels. These bands
are ordered from lowest to highest energy. The last band that is filled with electrons
in the ground state is called the valence band (VB). Energetically directly above, as the
first empty band, is the conduction band (CB). The distinguishing feature of a semicon-
ductor band structure is the noticeable gap between VB and CB.
23
2. Introduction
EvacEcEFEv
Egap
Figure 2.2.: Energy diagram for a typical n-type semiconductor. Showing the energy
levels for vacuum Evac, conduction band EC and valenace band EV, as wellas the Fermi engery EF and the band gap Egap.
In Fig. 2.2 a simple energy diagram for a typical semiconductor is shown. The filled
states are depicted in blue and are confined by the energy level of the valence band
EV. The empty bands between the energy level of the conduction band EC and the
vacuum level Evac are shown in red. The vacuum level describes the energy that is
needed to remove an electron from the system. Both are isolated by the bandgap
Egap. The Fermi level EF describes the energy level, which would have a 50% chance to
be occupied by an electron. It is located inside the bandgap.
The bandgap is a fundamental property to understand the photocatalytic process.
Photons can interact and excite electrons in the valence band and lift them over the
gap into the conduction band, leaving a hole in its place. The created electron-hole
pair, also called an exciton, is the source of the photocatalytic activity. In addition to
the energy difference separating the valence and conduction band, the gap type is
essential. To investigate the different kinds of bandgaps, the simple representation as
used in Fig. 2.2 is not sufficient. Describing the bands in more detail is not feasible in
normal space. Due to Heisenberg’s uncertainty principle, the exact energy and posi-
tion cannot be determined at the same time. With the help of the reciprocal space,
the problem can be transformed in such a way that it enables us to describe the mo-
mentum and energy at the same time. The wave vector k can be seen as a positionalvector in the reciprocal space. Based on the essential points in the first Brillouin zone,
the different possible energy states can be plotted as bands. In Fig. 2.3 band struc-
tures for two different phases of TiO2 are shown as examples. It is clear visible, that
the energy level of the valence and conduction band change with k. In the first graph
24
2.2. Heterogeneous photocatalysisshowing anatase, the maximum of the valence band (red dot) is not in the same posi-
tion as the minimum of the conduction band (blue dot). The bandgap is indirect. An
excited electron will need to change its momentum alongside its energy level. This
means that besides the interaction with the photon, the electron has furthermore to
interact with a vibration of the lattice (phonon interaction). This additional necessary
step lowers the efficiency of these kinds of materials. In contrast, in rutile (Fig. 2.3 b)
a direct bandgap can be found at the center of the Brillouin zone (Γ). A photon can
efficiently excite an electron directly to overcome the gap [64].
The presented band structures were calculated for the AFLOW4 repository [65] using
the density functional theory. Compared to experimental results, these calculations
underestimate the bandgap significantly. For the rutile phase, for example, the experi-
ment measures a bandgap of around 3.0 eV [66, 67], and the here shown calculations
estimates just 2.3 eV.
-4
-2
0
2
4
Γ X Y S Γ Z S1 N P Y1Z|X P
a)
Wave vector k
Energy
E–E F(eV)
Γ X M Γ Z R A Z|X R|M A
b)
TiO2 anatase TiO2 rutil
Figure 2.3.: Band structure of TiO2 in the a) tetragonal anatase phase and b) tetragonal
rutile phase, created from data provided by the AFLOW repository. The
red dots mark the lowest unoccupied state, while the blue dots mark the
highest occupied state.
4aflow.org – Automatic FLOW for Materials Discovery
25
2. Introduction
2.2.3. Interface between a semiconductor and a redox electrolyte
In the dark
The Fermi level describes an electrochemical potential for electrons. At absolute zero,
all energy levels below the Fermi level are occupied. The distribution of occupied /
empty states around the Fermi level is described in the Fermi–Dirac statistics.
FF(εe) = 1
exp
( εe–EFkBT)+ 1
(2.1)
If the energy of a band ismuch larger than the Fermi level Equation 2.1 is approximately
zero. The band is empty. In the case of much lower energy, the distribution converges
to one, and therefore these bands are filled. As mentioned above, if the energy level
of a band is the same as the Fermi level, it has a 50% chance to be occupied by an
electron. In a perfect semiconductor, the Fermi level would be in the center of the
bandgap, but impurities or doping shift this position. In n-type semiconductors, the
additional electrons in the conduction bandmove the Fermi level towards it. For p-type
semiconductors, the Fermi level is closer to the valence band. Further, the different
curvature of the valence and conduction band can influence the position of the Fermi
level.
The semiconductor is not isolated during the photocatalysis process. In our case, the
exciting aspect is the behavior of the material in conjunction with a solution containing
a pollutant. Between the redox pair and the semiconductor, an electronic equilibrium
will be established, as soon as they come into contact. The process is quite similar to
the combination of semiconductors and metals or differently doped semiconductors.
The reaction can be abstracted as a simple electron transfer between an oxidized (Ox)
and a reduced (Red) species.
Ox + z e–
Red {1}
Written in terms of electrochemical potential:
26
2.2. Heterogeneous photocatalysis
μOx + μe = μRed (2.2)
The Nernst equation is now used to describe the redox potential.
U = U◦–RTzF ln
CRedCOx (2.3)
U = U◦–kBTze ln
CRedCOx (2.4)
The redox fermi level can be defined relative to the vacuum level [68] (as recommended
by the IUPAC as a value of −4.4 eV is used [69]). With the standard reduction potential
U◦redox
based on the standard hydrogen scale we can write:
EF,redox = –4.4 eV – eUredox (2.5)
Uredox = U◦redox
–kBTze ln
CRedCOx (2.6)
EF ,redox = –4.4 eV – eU◦redox
+kBTz ln
CRedCOx (2.7)
As stated before, the Fermi level can be interpreted as the electrochemical potential of
the electrons. Because we investigate the system in an equilibrium state, the potential
of the electrons in the semiconductor and the redox system is equalized. When the
n-type example semiconductor would come into contact with a redox-pair with a lower
Fermi level, some electrons near the interface will switch over to the oxidized species in
the solution. This will lead to a depletion layer in the semiconductor and hence to the
bending of the bands near the interface. The resulting band structure at the interface
is very similar to a Schottky barrier that would be formed by a semiconductor/metal
interface [70].
27
2. Introduction
Evac
EcEF
EvEgap
Ebend
electrolyte
νh
δp0 Wdl Wdl + Lp
electrolyte
in dark under illumination
Figure 2.4.: Energy diagram for a typical n-type semiconductor in contact with an elec-
trolyte in dark and under illumination.
Under illumination
If a semiconductor is illuminated, photons can excite electrodes in the valence band.
The energy of the photon is proportional to its frequency ν. When enough energy
hν > Eg is transferred to the electron, it can jump over the bandgap into the conductionband. This leaves a hole in the valence band that behaves like mobile positive charge
carriers. The absorption coefficient α in the case of a direct bandgap is listed in Eq. 2.8.For an indirect bandgap Eq. 2.9 is valid. In these two equations A′ is a proportionality
constant. This relationship can inn addition be used to determine optical bandgaps
using a Tauc plot [71, 72].
α = A′(hν – Eg)0.5 (2.8)
α = A′(hν – Eg)2 (2.9)
Based on the definition of the absorption coefficient, we can make statements about
the penetration depths δp. The definition is based on the reduction of the initial irra-diation flux I0 by a factor of Euler’s number e. A variant of the Lambert-Beer law gives
the relation between the flux strength and the position in the material.
28
2.2. Heterogeneous photocatalysis
I(x) = I0 exp (–αx) (2.10)
Combined with the definition of the penetration depths, a simple relation can be es-
tablished.
I(δp) = 1
eI0 (2.11)
1
eI0 = I0 exp (–αδp) (2.12)
δp = 1
α (2.13)
From this relationship, we can conclude that penetration depths can be vastly differ-
ent depending on the type of bandgap that has to be overcome. A typical depth for
semiconductors with a direct bandgap is in the range of 0.1 to 1 µm. For materials
with indirect bandgaps, the penetration depths can be longer by order of magnitudes.
An example is gallium phosphide (GaP) at a wavelength of 515nm with a penetration
depths of 10µm [73].
For the practical usage of photolysis, it is crucial to investigate the fate of the created
excitons. The first question is how many of the new charge carriers are available to an
external system or circuit. The proportion between all created and collected carriers
are described by the quantum yield Φ. This critical parameter in the photochemistryis still a significant and not fully solved challenge to measure and to model. Alone
measuring the light that reaches the semiconductor is nearly impossible due to the
many different material layers in an experimental setup that can absorb or scatter the
light by themselves.
Despite the problems in modeling the quantum yield, it is possible to do an upper
limit estimation. Most important is the interactions near the interface between the
semiconductor and the electrolyte. In the exemplary n-type semiconductor, some of
the electrons are transferred into the electrolyte. Due to this shift, the band is bent
up toward the surface, as discussed in the dark section before. The width of this layer
that is depleted by the majority charge carriers is described by Eq. 2.14 based on the
density of donor/acceptor states Ns the relative permittivity of the semiconductor ε
29
2. Introductionand the potential difference by the bent bands Ebend [74].
Wdl = √2εε0EbendeNs (2.14)
The electric field separates Electron-hole pairs that are created in the depletion layer.
The minority charge carrier is moved towards the interface. In our example, the holes
are guided out, and the electrons are moving in the opposite direction, into the bulk
of the semiconductor. So the holes may react with the redox system in the electrolyte.
Pairs that are created away from the depletion layer are bound to recombination.
There is a chance that charge carriers still reach the depletion layer and, therefore,
the interface by diffusion before the recombination occurs. This depends on the life-
time τ of theminority charge carrier and theirmobility μ. In Eq. 2.15 the diffusion lengthfor holes Lp is defined [75].
Lp = √Dpτp (2.15)
Lp = √kBTμpτp (2.16)
These two dimensions must now be put in relation to the penetration depths δp. In Fig.2.4 the relative positions of all these lengths are presented. Because this is an upper
limit estimation, we can use the assumption that all separations that happen between
the surface and Wdl + Lp contribute to the carrier flow to the interface. The resulting
relation (Eq. 2.17) is the Gärtner equation [76].
Φ = 1 –
exp
(–Wdlδp)
1 +Lpδp
(2.17)
Φ = 1 –exp (–αWdl)1 + αLp (2.18)
This equation has many drawbacks that limit it as an estimation of the system. For
30
2.3. Photocatalytic materialexample, it is just valid if the electron transfer on the interface is fast. If the reaction is
slow, a build-up of the minority charge carriers will start to change the band structure.
A result of these flatted bands would be a significant increase in recombination in the
charged depletion layer that undercuts the assumption made in the beginning [70].
2.3. Photocatalytic material
2.3.1. Overview
In general, semiconductors are good candidates to exhibit photolytic behavior. As
explained in the section before, the bandgap that separates the valance and conduc-
tance band is a significant value. The wider the gap is, the more energy a photon
needs to create an electron-hole pair in the material. Bandgaps over 3.0 eV, for ex-
ample, lead to a photon absorption edge in the near ultraviolet (UV) region. Figures
2.5 - 2.7 shows the wide range of possible wavelengths. The illustration is based on
Aracely Hernández-Ramírez and Iliana Medina-Ramírez [77] extensive compilation of
photocatalytic material properties.
The most commonly used materials can be found under the metal oxides. TiO2 and
ZnO are prominent members of this group and from particular interest in this thesis.
As such, they will be described in more detail in separate sub-sections following this
overview.
One interesting example of this group on the high end of the energy spectrum (5.0 eV)
is zirconium dioxide (ZrO2). As a stable and already widely used oxide in ceramic tech-
nology, it is very well studied. Based on the high bandgap, the produced electron-hole
pair has a high chemical potential. Besides, the bandgap can be modified significantly
through the preparation of the material [78]. Compared to TiO2 the photolytic activity
of ZrO2 is quite low [79]. Another drawback is the absorption edge at 248nm, which
means solar irradiation cannot be used with this semiconductor.
The second example is tungsten trioxide (WO3), in which the absorption edge is further
shifted into the visible spectrum compared to TiO2 and ZnO. With a bandgap of 2.8 eV
up to 8.5%of the solar spectrum could be utilized. Besides, the possible use of sunlight
WO3 is equally interesting because it is very stable under many conditions, like strongly
acid solutions [80]. The photocatalytic efficiency of pure WO3 is limited due to the
Figure 2.7.: Bandgap energies and absorption edges for selected ternary (•) and qua-ternary semiconductors (N) [77].
An astonishing number of semiconducting materials were tested in the last decades
for their photocatalytic properties. Ternary and quaternary semiconductors like met-
allates, oxysulfides, oxyhalides, oxynitrides, or oxysulfide represent a large portion of
all potential photocatalytic material (Fig. 2.7). Some of these materials show promising
properties for water splitting. However, for use in water detoxification, none of the
materials can rival the properties of TiO2 if UV radiation is considered. In the reviews
by Hernández-Alonso et al. [86] and Di Paola et al. [87] the properties of the further
photocatalytic materials is collected. A recollection of this information here would go
beyond the scope of this work.
33
2. Introduction
2.3.2. Titanium dioxide
Since the publication by Fujishima andHonda in 1972 [62], titaniumdioxide TiO2 repre-
sents still the highest echelon for photocatalyticmaterial. Any newmaterial is inevitable
compared to this standard. In this work, TiO2 will as well serve as the foundation.
Titaniumdioxide is a solid that ismostly prepared as a powder with a very brilliant white
color due to the very high refraction index of 2.6. It is odor- and tasteless. The oxide
is very stable in a wide variety of environments and unsolvable in water. Commonly
the material consists of a mixture of different crystalline types. Although TiO2 can be
forced into multiple different phases, two are of significant interest.
Unit cell:
c = 2.9587 Å
RutileSpacegroup: P42/mnm
a = 4.5937 Å
a)
Unit cell:
c = 9.5143 Å
AnataseSpacegroup: I41/amd
a = 3.7845 Å
b)
Figure 2.8.: Crystal structure of (a) rutile (8 unit cells) and (b) anatase (4 unit cells) from
different perspectives.
First rutile, the most commonly occurring natural form of titanium dioxide. The cristal
structure is tetragonal (P42/mnm) as shown in Fig. 2.8 a. Two atoms form the unit cell
of this structure together. Every titanium atom is surrounded by six oxygens forming
connected octahedrons. Each octahedron is in contact with ten others (two edge and
eight corner connections). It is worth noting that the octahedrons are slightly distorted.
Based on this cristal system the bandgap has a value of around 3.0 eV (see Fig. 2.3 a)
[88]. The density of rutile amounts to 4.13 g cm−3 [89].
Second anatase, the crystal phase that is commonly linked to a higher photocatalytic ac-
34
2.3. Photocatalytic materialtivity. The crystal structure is tetragonal (I41/amd) as shown in Fig. 2.8 b similar to rutile.In contrast to rutile, four atoms are located in the unit cell, and the octahedrons are
stronger distorted. While the octahedron structure stays the same, the interconnec-
tion changed. So are in anatase each octahedron in contact with just eight neighbors
(four edge and four corner connections). This results in altered distances between
Ti-Ti (extended) and Ti-O (shorten). Overall the density is reduced by 0.37 g cm−3 to
3.76 g cm−3 compared to rutile [89]. The bandgap is also slightly elevated to 3.2 eV.
While the valence band edge is very comparable between both materials is the con-
ductance band is roughly 0.2 eV higher in anatase [67].
The thermodynamic stabilities of the different titanium dioxide phases are quite sim-
ilar. Due to the small disparities, the stability order for macrocrystalline systems is
rutile → brookite → anatase. While annealing at temperatures below 400 °C will yield
anatase at higher temperatures (over ~600 °C), rutile becomes the dominant phase.
In the case of nanomaterial, surface energy plays an important role. For tiny particles
under 11nm, anatase is themost stable configuration. If the particle size is over 35nm,
rutile is again the most stable phase. In between, the brookite is most favorable [90,
91]. While it is still heavily debated if anatase or rutile is the superior photocatalytic
material, it seems very clear that a mixture of the two phases shows highly beneficial
properties [92]. The practical standard for photocatalytic materials Degussa’s P25 is
likewise a mixed-phase product. It is compiled form 75% anatase and 25% rutile. The
primary challenge in understanding the performance of P25 is to characterizing the
powder. So far the precise distribution of the phases and the surface futures is still
not fully understood. The general explanation regarding the enhanced activity refers
to the interfaces between both phases as the cause of the cooperative effect. This is
one of the reasons, while ultrasonication of P25 shows just a very limited effect [93].
While the accessible surface area is highly increased, and the efficiency of photon ab-
sorbance is improved by separating the particle agglomerations, the overall reaction
rate is just raised slightly. Possible explanations of the effect include the formation
of heterojunctions, due to the different band configuration. Besides, charge transfers
between the phases through band bending is likely [88].
Using TiO2 brings the significant benefits of a very well established material. Through
its high usage, the interaction with the environment and humans is well investigated. In
2015 the worldwide estimated consumption was 5.89 million tonnes, but just around
10 thousand tonnes are attributed to nanomaterials [94]. Primary use cases can be
found in the paint and coatings industry (55%), as filler in polymers (26%) and paper
35
2. Introductionproduction (8%). In the remaining 11% are mostly applications in the textile industry,
ink production, food preparation, cosmetic formulation, and as a catalyst [95]. Primar-
ily through the use in the cosmetic and food industry is titanium dioxide well tested. As
food additive (E171), it is categorized in the European Union in “Group II: Food colours
authorised at quantum satis5”. As food color, it shares this group with a few other sub-
stances like Beetroot Red (E162) or caramel (E150). It can be found in nearly all daily
foods that need white color or to be brightened from prominent products like tablets,
chewing gum, cheese, ice cream, noodles over flavored drinks, and cocktails to salads
and fine bakery wares [96]. As a result of an intensive discussion about nanomateri-
als in cosmetic products around the year 2007 in the EU, an extensive safety report
about nano-scale titanium dioxide in suncream was compiled over the next years [97].
It is important to note that the investigated studies in this report mostly concerned
coated material. Furthermore, TiO2 powder produced for UV protection in cosmetic
has been optimized to show as little photocatalytic activity as possible. Therefore, it
is still necessary to ensure that any application with titanium dioxide releases as little
material as possible into the environment.
2.3.3. Zinc oxide
The high similarity with TiO2 brought ZnO quickly in the spotlight of the photocatalytic
research [98]. Even with just 41% of the recent publication count compared to tita-
nium dioxide6, it is still the second most published about photocatalyst.
Zinc oxide is a white, odorless n-type semiconductor that is commonly available as
a powder, but single crystals can be produced as well. It is practically unsolvable in
water. Growing ZnO on a cubic lattice can produce a zincblende structure, but this
configuration does not play an essential role in photocatalysis. The most important
crystal structure is wurtzite, that is formed at ambient condition. As shown in Fig. 2.9
the crystal is hexagonal (P63/mc). Each zinc is surrounded by four oxygen. This tetra-hedral coordination is also accurate from the perspective of an oxygen atom. The
direct bandgap is similar to TiO2 with 3.37 eV [99]. ZnO needs, therefore, near UV ir-
radiation to show photocatalytic activity. Due to the non-centrosymmetric structure,
piezoelectric properties can be observed in zinc oxide [100].
The global production of zinc oxide was estimated at 1.37 million tones for 2014 [101].
5as much as is sufficient6Indexed in Scopus for the year 2017
36
2.3. Photocatalytic material
Unit cell:
c = 5.307 Å
ZnO WurtziteSpacegroup: P63/mc
a = 3.289 Å
Figure 2.9.: Crystal structure of zinc oxide - wurtzite (9 unit cells) from different per-
spectives.
Nano-sized materials account, however, just for several thousand tones [94].
Its impact on the environment limits the use of ZnO to degraded organic components
in wastewater. In the literature, many different perspectives on the topic are available.
In a review in 2016 Lee et al. [99] stated about ZnO:
“ZnO is an environmental friendly material as it is compatible with living
organisms, which lending itself nicely to a broad range of daily applications
that will not leave any risks to human health, and environmental impacts”
This is a strong claim, that is disappointingly not corroborated with references. In an
eco-toxicity comparision between TiO2, SiO2 and ZnO by Adam et al. a different picture
emerges [41]. There, it is clear that ZnO has the strongest influence on the growth
of the studied test organisms (Gram-positive Bacillus subtilis and Gram-negative Es-cherichia coli). Furthermore, the classification of zinc oxide as hazardous to water (WGK2: wassergefährdend) in Germany shows that the usage of ZnO requires special care,
to reduce the chance of environmental contamination [102]. In the European Union,
ZnO is classified as hazardous to aquatic systems (Aquatic Chronic 1 | H410: Very toxic
to aquatic life with long lasting effects) as well. While many studies show the effect of
zinc oxide on systems like microorganism, algae, or zebrafish embryos, the overall
ecotoxicological knowledge is still not sufficient to extrapolate to other circumstances
[103].
37
2. IntroductionA further drawback of ZnO is the existence of anodic photocorrosion, which is espe-
cially problematic at lower pH values. The reaction sequence is listed below [104].
ZnObulk + 4 νh ZnObulk + 4e–+ 4h
+{2}
O2–s + h
+O
–s {3}
O–s + O
2–s + h
+(O O)
2–{4}
(O O)2–+ 2h
+O2 {5}
2 ZnO + 4 νh 2Zn2+(aq) + O2 + 4e
–{6}
During the process, the surface oxygen Os is detached from the bulk oxide. This pro-
cess reduces the catalytic activity of ZnO over time. Besides, Zn2+ ions will be released
into the environment at higher levels than possible by usual dissociation. This release
is especially problematic for the environment because Zn2+is allegedly the main rea-
son for the ascertained toxicity of ZnO. Different strategies are available to reduce the
effect. For example, passivation of the surface with polyaniline reduced graphene ox-
ide or fullerenes. Optimization of the exposed crystallographic surface influences the
strength of the effect [99].
Zinc oxide can be produced in a wide variety of morphologies [105]. The availability of
specific nanostructured surfaces is very promising for use in complex photoreactors.
The generation of column-to-rod morphological transitions, oriented nanocolumns,
and nanoplates can help to optimize surface area and to reduce photocorrosion.
Zinc oxide often presents a higher photocatalytic activity compared to titaniumdioxide.
The problems regarding photo-corrosion and solubility in strong acids and alkalismake
it challenging to including ZnO in a water cleaning system. All in all is zinc oxide is a
good model system in tandem with titanium dioxide.
38
2.4. Light sources
2.4. Light sources
2.4.1. Solar
Solar irradiation is a universal source of energy available everywhere on earth in vary-
ing intensities. The idea of utilizing this source as efficiently as possible is gaining now
more andmore popularity. As stated in the historical introduction into heterogeneous
photocatalysis, it was already realized at the beginning of the 20th century that solar
irradiation is a promising energy source for chemical processes [63]. Nowadays, this
route in chemical synthesis is rediscovered in combination with the use of photocat-
alytic material to enable new pathways [106].
For the cleaning of wastewater, the usage of solar irradiation enables unique advan-
tages. First, the cleaning setup can be designed without the need for a highly reliable
electronic power-grid. Second, no additional burden on the environment through the
use of toxic materials common in some lamps like mercury. The final advantage is the
low running cost.
The most common photocatalytic materials can use a small portion of the solar spec-
trum. Titanium dioxide, for example, can utilize between 4.5% and 7.5% of the avail-
able solar irradiation (depending on the bandgap) [107]. Due to different drawbacks,
photocatalysts with a naturally smaller bandgap are rarely used. The main focus in
visible light photocatalysis is placed on the improvement of the established materials.
Many different strategies to treat TiO2 are available [108, 109, 110].
One approach is the combination with other photosensitive semiconductors. Two
main prerequisites are necessary for such a combination. First, the light absorption
edge of the added semiconductor needs to be well in the visible range. Second, the
level of the conduction band of TiO2 needs to be lower than the one of the added sen-
sitizer. This is important to enable an excited electron to pass easily from the added
semiconductor onto the titanium dioxide. A system formed from nanosized TiO2 and
cadmium sulfide (CdS) exhibit such a behavior [111]. There the photo-generated elec-
trons generated in the sensitizer (CdS) can be efficiently transferred to the conduction
band of titanium dioxide. This electron transfer enables an effective decomposition of
contaminants under visible light.
Doping is a useful tool to alter the properties of semiconductors. With the addition of
39
2. Introductionmetal ions, new states can be introduced inside the bandgap. Often transition metals
are used since their redox energy states lay in between the bandgap of TiO2. The new
states introduced close to the valence or, respectively, the conductance band leads to
a redshift and therefore enables visible light absorption. Dopant concentrations need
to be optimized carefully, as quickly unwanted effects can overshadow the achieved
improvement. Mainly the introduction of new recombination sites causes problems,
reducing the average lifespan of the excitons, and therefore reducing the maximum
length they can diffuse. Electron-hole pairs created further away from the surface are
lost for the reduction of pollutants.
Non-metal ions can be beneficial dopants for TiO2 as well. While there is work on us-
ing a wide range of elements like fluorine, iodine, or phosphor as dopants, the primary
attention is focused on nitrogen and carbon. Sato discovered in 1986 [112] that the
addition of ammonium hydroxide (NH4OH) into the preparation process of TiO2 en-
ables a respond under visible light. In 2001, Asahi et al. [113] restarted the interest in
nitrogen as a dopant. It could subsequently be shown that an N-doped TiO2 material
can achieve an up to nine-time better degradation of methylene blue compared to
P25 in visible light (>450nm) [114].
One way to introduced carbon into titanium oxide is during the preparation via flame
pyrolysis [115]. Depending on the used fuels (glycine, hexamethylenetetramine, or ox-
alyldihydrazide), a significant change of the bandgap can be reached. With glycerin as
fuel, the absorption edge could be pushed to 435nm with a slow reduction of adsor-
bents until 560nm. This redshift covers a more substantial part of the solar spectrum,
compared to pure titanium dioxide. While the activation in the visible light is favorable,
it needs to be noted that the oxidation power and mobility of the generated holes
are lower than in pure TiO2. The combination of p- and n-dopant like nitrogen with
fluorine is an opportunity to stabilize the material system and reduce the increased
exciton recombination typical for doped materials. This co-doped systems still work
efficiently under visible light [116].
Besides incorporating elements directly into the structure of titanium dioxide, decora-
tion of the surface can have a considerable influence on the photocatalytic properties.
The introduction of noble metal clusters on the surface enhances foremost the life-
time of excitons, as they act as electron traps. They can be beneficial in shifting the
light absorption edge aswell. Particular experiments with silver showpromising results
[117]. One possible explanation presented in the published work is surface plasmon
absorption from the silver cluster.
40
2.4. Light sources
irradiation in W/m2
125
250
150
175
200
225
100
500 km
Direct horizontal
Figure 2.10.: Long-term average of direct horizontal irradiation (solar radiation re-
ceived from above by a surface horizontal to the ground) for central Eu-
rope (top) and south-east Asia (bottom). Solar resource data obtained
under "Creative Commons License Attribution 3.0 IGO" from the Global
Solar Atlas, owned by the World Bank Group and provided by Solargis.
The design process needs to be optimized for it from the start to use solar energy effi-
ciently in the photocatalytic process. Often a collector is necessary to reach a suitable
energy concentration in the reaction container. The problem of efficient solar collec-
tors is an intensely discussed topic [118, 119]. The parabolic-trough collector (PTC)
[120], and the compound parabolic collector (CPC) [121] are often used photocatalytic
applications. What becomes quickly apparent when dealing with solar collectors is the
necessary space to assemble such structures. Solar driven systems can only be incor-
porated in locations that can provide this space.
Another obvious drawback is the dependence on weather and daylight. Processes
that need to be continuous, for example, urban wastewater treatment or industrial
around the clock production, cannot be covered. This limits the use of solar light for
41
2. Introductionwater cleaning to situations, where the contaminated water can be stored temporarily
overnight and in case of unfavorable weather.
To assess if solar is a suitable solution, the location of a system’s deployment plays
a crucial role. Most parts of central Europe receive just sparse solar irradiation on
average over the year. In particular, during the winter, system performance would
be reduced severely. A comparison between central Europe and south-east Asia in
Fig. 2.10 demonstrates the quantitative difference in available solar energy. While a
solar-based reactor to reduce the concentration of organic dyes in the effluent of the
textile industry in the south of Vietnamwould be sensible, a similar project in Germany
would not be feasible. The best conditions exist in the desert regions around the tropic
circles. Nevertheless, the needs in these parts of the world are generally different from
the possibilities provided by this technology.
2.4.2. Fluorescent tubes and mercury-vapor lamps
As discussed previously, the most common photocatalytic materials need light in the
UV range. Artificial light sources with a wavelength below 400nm are needed to enable
a continuous process. The most famous UV-lamp is the so-called “blacklight.” These
lights are constructed like typical fluorescent tubes. A low-pressuremercury-vapor gas-
discharge lamp forms the base. Under low pressure, the two dominant spectral lines
emitted are at 185 and 254nm. Both lines would be harmful in normal circumstances,
due to the formation of ozone and possible damage to skin and eyes. In the “blacklight”
the emission at 254nm is converted by the phosphors material covering the inner
lamp tube. A typical phosphor that is contained in the lamps used for the experiments
described in this work is strontium tetraborate doped with Europium (SrB4O7:Eu). The
excited phosphor emits a 20nmwidth peak at 372nm [122]. Wavelengths outside the
desired window are filtered so that the tube glows in a deep purple. The energy from
the 185nm peak cannot be used with this kind of lamp and is lost to heat. This lamp
type is useful for experiments because no extensive security measures are needed,
and the wavelength is close to the absorption edge of the conventional catalysts ZnO
and TiO2.
If the phosphor layer is omitted and fused quartz glass used the UV emission of the
low-pressure mercury-vapor lamp can be used directly. As stated above, this kind of
lamp should only be used in a controlled environment. High efficiency of around 35%
42
2.4. Light sourcescan be reached due to the missing conversion step and filters. Most of the energy is
converted into light at a wavelength of 254nm. The ozone generated from the deep
UV-light can be used to create a synergistic effect with the photocatalysis [123].
Overall, mercury vapor based lamps are cheap and effective. Reactor systems based
on these tubes are limited in their design choices because the smallest available com-
mercial diameter is around 15mm.
2.4.3. Light-emitting diodes
Light-emitting diodes (LED) are semiconductor devices that allow electric current to
pass through in only one direction. In a diode, two semiconductors are forming a
p-n-junction. When a LED is operated with a forward bias, recombination occurs at
the interface between the electron-rich (n-type) and electron depleted (p-type) layer
generating light. In conventional diodes, the recombination generates just heat.
H. Round reported the first indication that the production of light from a semiconduc-
tor is possible in 1907 [124]. While studying the diode nature of siliciumcarbid Round
observed a faint yellowish light emerging from his sample. It took nearly 50more years
until, in 1955, R. Braunstein demonstrate infrared light generation with a LED [125].
He linked the observed wavelengths produced by gallium antimony (GaSb), gallium ar-
senide (GaAs), indium phosphide (InP), and germanium-silicon (Ge-Si) alloys directly to
the recombination of the charge carrier and the bandgap of the materials. This lead
finally to the first commercial product, whose ancestors can still be found in remote
controls to this day. The jump to visible light succeeded in 1961 with Ga(As1–xPx) pro-
ducing red light at 710nm [126]. During the 1980s and 90s, the race towards a blue
LED took place. In 2014 Isamu Akasaki, Hiroshi Amano, and Shuji Nakamura received
the Nobel Prize in Physics for their work on for “the invention of efficient blue light-
emitting diodes which has enabled bright and energy-saving white light sources.” The
problematic gallium nitride system was, in the end, the key to a bright blue LED [127].
The development of LEDs in the near UV (300-400nm) and deep UV (200-300nm)
started around 2000 [128]. While the development was mainly driven by the idea to
create an improved white LED through the combination of a near-UV LED with a phos-
phor mixture, today, UV LEDs start to replace the traditional mercury vapor based
solutions even in industrial applications. This trend is accelerated by the “Minamata
Convention on Mercury” from 2013, where many nations pledged a reduced usage
43
2. Introductionand trade of mercury [129]. The success of UV-LED is based on their rapid develop-
ment over the last years. In 2002 the best UV-LED at 365nm achieved an output of
about 0.108W. Ten years later, the output of high powered UV-LEDs was already over
100fold at 12W [128]. The achievable wall-plug efficiency of over 22% at 365nm up
to 77% at 415nm makes LED very attractive for photocatalytic applications [130]. Be-
sides the higher efficiency, LED-solutions exhibit a longer lifetime (in the near UV), a
stable intensity over the product life and are easier to integrate, due to smaller foot-
print and more manageable heat and temperature requirements.
2.4.4. Organic light-emitting diodes
The basic work principle for organic light-emitting diodes (OLED) is close to the LEDs.
Instead of an inorganic semiconductor is the emissive electroluminescent layer formed
by small organicmolecules or polymers. These building blocks enable the use of simple
and flexible substrates and a wide variety of sizes and designs.
OLED could have a significant impact on the design of photocatalytic reactors. The
possibility to stack light generation and photocatalytic material over a wide area with
a minimal thickness could enable new designs. Thin layers of catalyst would be backlit
from a central OLED core.
While the development of near-UV range OLED is on its way, the technology is still not
ready for integration [131, 132, 133, 134]. Looking back on the development history
in the field of LEDs and their struggle with the high energetic blue and UV light, it is
not far-fetched to anticipate the disruptive shift powerful UV-OLEDs could have. At the
moment, the main drawbacks is the energy output and the far too short lifetime of the
modules.
44
3. Materials and methods
3.1. Analytic methods
3.1.1. Nanoparticle characterization
The nanoparticles were characterized for the following parameters: surface area, tex-
ture and diffuse reflectance spectra. The specific surface area of the particles was de-
termined by the Brunauer-Emmett-Teller (BET)method [135]. Thismethod is based on
the theory on multilayer gas adsorption presented by the three name-giving authors
in 1938 [136]. Measurements of the adsorbed gas amount on the external and acces-
sible inner surface under different parameter sets are conducted. With multiple such
measurements, the adsorption isotherm (Eq. 3.1) can be used to extract the specific
amount of gas adsorbed in a monolayer covering the entire surface. The investigated
material must not absorb the chosen measuring gas. That inaccessible pores cannot
be measured with this method is not problematic in this use-case, as pollutants would
not be able to reach these spaces.
pna (p0 – p) = 1
nmCBET +CBET – 1nmCBET · p
p0 (3.1)
The textural properties of the photocatalytic nanoparticles were analyzed by nitrogen
adsorption-desorption at its boiling point (77 K) in a Micromeritics TriStar analyzer (Mi-
cromeritics, Norcross GA). Before performing adsorption experiments, samples (0.5 g)
were outgassed at 26.7 Pa and 350 °C for 6 h.
45
3. Materials and methodsIn the same year as the theoretical foundations of the BETmethod was laid, the first ar-
ticle about the scanning electronmicroscope (SEM) was published [137] with an image
of a ZnO crystal surface. In the SEM, a super fine electron beam is scanning in a raster
over the probe surface. Through the recording of the backscattering and secondary
electrons emanating from the surface, an image can be created. SEM reaches magni-
fication in the order of 100000 which is significantly higher than transmission light mi-
croscopy but lower than high-resolution transmission electron microscope. The mor-
phology for both used particle types was analyzed with an SEM operated at 10 kV and
25 kV.
As the final analytic method for the photocatalytic nanoparticles, diffuse reflectance
spectroscopy was used [138]. This method is based on the theory from Kubelka and
Munk from 1931 aimed towards colored paints [139]. It describes the radiation flux Iinto a body that can both scatter and absorb. Split into infinitesimal small layers of
thickness dx the fluxes in the direction of the initial irradiation I and the opposite di-
rection J is described in Eqs. 3.2 and 3.3.
–dIdx = –(K + S) I + S J (3.2)
dJdx = –(K + S) J + S I (3.3)
A solution for these differential equations was found by Kubelka some years later [140].
The general solution is presented in Eq. 3.4.
R = 1 – Rg [a – b coth(bSt)]a – Rg + b coth(bSt) (3.4)
a = 1 + K/Sb = √a2 – 1
In the solution, t is the thickness of the sample, and Rg is the reflectance of the back-ground material the sample is placed upon. In practice, the samples are beyond a
critical thickness which renders the background obsolete. For t → ∞ the hyperbolic
cotangent approaches 1 and Rg = 0. The resulting Eq. 3.5 is also known as Kubelka–Munk function FK,M.
46
3.1. Analytic methods
FK,M(R∞) = KS = (1 – R∞)2
2R∞(3.5)
In the case that the scattering is not depending on the wavelength, FK,M(R∞) is propor-
tional to the actual absorption spectrum. For samples with grain sizes over 1.5 µm, it
was shown that this assumption is true [141]. In the experiments with smaller grain
sizes the scattering coefficient increases significantly in the UV region. That results in
a damped response the further the measurement reaches into the UV and the peak
of a measurement is shifted to shorter wavelengths.
The spectra for the material used were obtained with an UV-vis spectrophotometer
2101PC (Shimadzu) in the range of 190 to 600nm. It was equipped with a diffuse
reflectance attachment and a reference standards disks made from pressed barium
Absorption spectroscopy is widely used to quantify the concentration of a large num-
ber of different molecules. The spectra are typically measured for wavelengths in the
range from 200 to 800nm. Depending on the molecule, a subset can be selected to
speed up the measuring process.
The method is based on the Beer–Lambert’s law (Eq. 3.6) describing the connection
between transmittance T , sample thickness t, and sample concentration Cs.
A = – log TL = logIiI = εtCs (3.6)
This equation can be used directly if the sample could be held in a perfect transparent
container. In practice, the light beam has to pass through the air as well as the cuvette
material and cross the interfaces between air, cuvette, and sample twice. To account
for these effects, the intensity of the sample Isample is measured in relation to the in-
tensity of the beam passing through a comparable setup filled with the solvent only
Isolvent. With Eq. 3.7, a close approximation of the actual absorbance and transmittance
47
3. Materials and methodsis calculated [142].
IsolventIsample ≈ IiI (3.7)
For most organic molecules, the relation between the concentration and the observed
absorbance is linear, following Beer–Lambert’s law. However, this linear behavior is
limited to low concentrations (< 0.01mol L−1). At high concentrations, themolecules do
not act isolated from each other anymore, and the absorption of light in one molecule
can influence the state of its neighbors. Some molecules exhibit non-linearity already
at lower concentrations. The cation of methylene blue, that is used as an example
molecule for dyes in this work, does not show adherence to Beer–Lambert’s law even
at a concentration under 1 • 10−6mol L−1. In this case, a densely populated calibration
curve is used, to not rely on linear dependency [143].
In all experiments, the samples were analyzed using a CARY-100 UV-vis (Varian) spec-
trophotometer. The concentrations were determine by comparing the measured ab-
sorption spectra to the calibration curves.
3.1.3. SPE-HPLC-MS/MS
UV-vis spectrometry is limited to simple systems with a low variety of substances. The
effluent of a sewage treatment plant contains a high number of differentmolecules in a
single sample. Besides, the low concentrations of these substances provides a further
challenge. Therefore, R. Gurke et al. developed a novel method at the Institute of Clin-
ical Pharmacology in Dresden, which is based on three main techniques [144]. In the
first step, a sample is prepared using solid-phase extraction (SPE). By letting the sam-
ple run through a solid phase that the solvent can pass unimpeded, the investigated
substances are adsorbed, and the molecules of interest are enriched. This allows for
the analysis of very low concentrated samples. In the next phase high-performance
liquid chromatography (HPLC) is applied. Thereby, the molecules are spread based on
the interaction with the material in the columns. Through this process, the following
analytic method is utilized more efficiently. The concentration is then measured by a
tandemmass spectrometry (MS/MS). The combination of two mass spectra allows the
first to preselect a mass range from the fraction generated by the HPLC for detailed
48
3.1. Analytic methodsanalysis in the second one.
The developed SPE-HPLC-MS/MS-method is described in detail in Gurke et al. 2015
[144]. The following summary is based on the joint publication with R. Gurke [145].
From the solutions generated in the experiments 1mL of the sample was taken, ad-
justed to a pH of 3 by using formic acid and spiked with 100 µL of the internal stan-
dard (IS) solution (10µg L−1). The samples were extracted using an Abimed ASPEC XL
(Gilson) withOasis HLB 10mg Extraction Cartridges (Waters). Under a gentle air stream
at 50 °C the eluates were evaporated to dryness and re-dissolved in 250 µL mixture of
solvent A and solvent B (80/20, v/v). The solvents A (97/3/0.05; v/v/v) and B (5/95/0.05;
v/v/v) were a composition of 2mmol L−1 ammonium acetate solution, acetonitrile, and
formic acid. An LC-MS/MS system, consisting of a Dionex-HPLC composed of an Ul-
tiMate3000 Pump and Autosampler (Thermo Fischer Scientific) with a Chromeleon 7
Chromatography Data System (Dionex Softron) and coupled to an API 4000 tandem
mass spectrometer (AB Sciex) equipped with an electrospray ionization source (ESI),
was used for the analyses of the samples. The chromatographic separation was per-
formed with a Synergi 2.5u HydroRP 100A, 100 x 2.0mm column and a C18 security
guard 4mm x 2mm (both Phenomenex) using a multi-step gradient out of solvent A
and B with a total runtime of 15min. For the analyses, an injection volume of 20 µL
was chosen. The mass spectrometric analyses were performed in multiple reaction
monitoring (MRM)mode with positive electrospray ionization. The Analyst data system
version 1.6 (AB Sciex) was applied to control the MS, evaluate the peak area, analyze
the regression of calibration curves, and calculate the final concentrations.
3.1.4. Non-purgeable organic carbon
To analyze the performance of a photocatalytic system, the concentration evolution
of the initial molecule is not sufficient enough. The tracking of all intermediates would
be the preferred solution but is practically impossible for complex organic molecules.
However, measuring the overall amount of organic carbon instead allows for monitor-
ing the degradation process in its entirety.
To limit the measured carbon to the organic fraction, solved inorganic carbon need to
be removed. As shown in Reac. 7, the carbonic acid reaction can be moved towards
dissolved CO2 by acidifying the solution. Through bubbling the solution with O2, the
inorganic carbon is purged.
49
3. Materials and methods
CO2 (aq) + H2O(l) H+(aq) + HCO
–3 (aq) {7}
Subsequently, the remaining non-purgeable organic carbon (NPOC) is quantified [142]
using a multi N/C 3100 from jena analytic. The sample is broken down, by injecting
it into a combustion tube, that is filled with catalyst and heated to 800 °C. A non-
dispersive infrared sensor measures the produced CO2 concentration. The carbon
dioxide concentration integrated over time can be related to the carbon content in
the sample.
3.2. Experimental investigations
3.2.1. Model substances
The antibiotic ciprofloxacin, and the dye methylene blue were selected as model sub-
stances. A core requirement for the selection was a significant peak in its absorption
spectra for the use with an UV-vis absorption spectrometer.
Ciprofloxacin (C17H18FN3O3) is a synthetic antibiotic from the fluoroquinolone group
developed by Bayer. This antibiotic is most effective against Gram-negative bacteria.
Its bactericidal effect is based on the inhibition of enzymes essential for cell division.
While themedical indications to use this drug are reduced significantly in the last years
through to newly discovered side effect, it is still in use for a wide area of bacterial
infections. A typical dose is 1 g d−1, that results in a serum concentration of around
2.5mgL−1. With a typical half-life of 4 - 7 h, the drug is excreted over the kidneys.
Over 69% of the given dose leaves the body unaltered (44.7% urine, 25.0% feaces).
Another 19% are discharged as close metabolites [146]. When the drug reaches the
wastewater system, it is diluted significantly but is still quantifiable. In the influent of
the Dresden wastewater treatment plant (WWTP) a concentration of 422ng L−1 was
measured [147]. As stated before, the removal of antibiotics from our wastewater is
essential to prevent the development of resistances against them. Mutations in the
target enzymes, topoisomerase II and IV can result in resistance against ciprofloxacin.
Multiple simultaneous mutations can lead to a more broad clinical resistance against
the whole class of similar antibiotics. The presence of antibiotics in the environment
50
3.2. Experimental investigationscan apply a selection pressure on bacteria even outside of a therapeutic context.
Methylene blue (C16H18ClN3S) was selected as an example of an organic dye. This syn-
thetic cationic dye was first produced in 1876. The deep blue color is mostly used to
dye cotton in the textile industry. It is still in use today, even though the high number of
available dye variants naturally limits its use. While the textile industry consumes the
most substantial portion of methylene blue, its interaction with tissue is the main rea-
son for its detailed scientific examination. Very early methylene blue was already used
to stain biological systems. The discovery of its strong interactions with pathogens led
to its use as an anti-malarial drug in 1891. Methylene blue can, therefore, be seen
as the first synthetic drug. Its selective affinity for nervous tissue made it useful in
the treatment of neuropsychiatric disorders. A great variety of drugs were developed
based on methylene blue [148, 149]. Due to its prominence in the biological field, it
was a natural choice early on as a model substance. Over the decades, it became a
standard for testing photocatalytic degradation processes.
3.2.2. Adsorption-desorption
To understand the dynamics between the adsorption and desorption, experiments
conducted in darkness are necessary. The entire reaction vessel was sleeved with
aluminum foil, and the laboratory was just scarcely illuminated to limit the possible
introduction of light during the sampling procedure.
In the initial experiments 60mL of prepared solution of ciprofloxacin (12.5 µmol L−1)
and methylene blue (11.0 µmol L−1) were filled in 100mL beakers (VWR) and continu-
ous stirred. To those solutions, 1 g L−1 of TiO2 P25 (Evonik) or ZnO (IOLITEC Ionic Liq-
uids Technologies GmbH) was added. The first sample was taken with a syringe 40 sec-
onds after the photocatalytic nanoparticles were mixed in with the solutions. Multiple
further samples were taken over the next half hour every few minutes. The nanoparti-
cles need to be removed to stop further adsorption. The sampleswere passed through
a fine filter (Rotilabo nylon, pore size 0.2 µm). In preparation for the following UV-vis
analytic, the remaining nanoparticles were removed by double centrifugation for 60
minutes. The final supernatant was then measured.
As discussed further in the introduction to the single organic species model (p. 75),
the first measurement is the most important to determine adsorption constant (Eq.
3.18). The experiment was repeated additional five to ten times for each combination
51
3. Materials and methodsof material and catalyst to improve the reliability of the measurements. In these addi-
tional experiments just the initial concentration and the result after 40 seconds was
recorded.
3.2.3. Photocatalytic degradation
The degradation experiments were carried out in 100mL beakers from VWR with a
5 cm diameter. They are made from borosilicate glass with a wall-thickness of 3.3mm
and are therefore well suited for experiments involving UV-light. The illuminating de-
vice, manufactured by UMEX, was equipped with 6 Philips 8W mercury fluorescent
tubes. Two beakers were placed in 15 cm distance from the illumination device, with
an equal distance away from the center. The UV intensity inside the beakers ranged
from 18 to 19Wm−2 and was determined by a UV34 Lux Meter (PCE). The full setup is
shown in Fig. 3.1.
Figure 3.1.: Experimental setup for the photocatalytic degradation experiments - the
beaker on the right side does not contain photocatalyst and serves as a
control.
Prior to the start of the degradation experiments, samples were stirred in the dark for
at least 30 minutes. Thereby, the solution reaches the adsorption-desorption equilib-
rium between the organic molecules on the photocatalyst surface and in the solution.
An amount of 50mL of this solution was then exposed under continuous stirring to UV-
radiation with an intensity peak at 365nm. The specific spectrum of the light source is
incorporated in Fig. 4.1.
52
3.2. Experimental investigationsSamples were taken from the solution at multiple points in time to analyzing the tem-
poral degradation of organicmolecules. The same filtering and centrifugation steps, as
described in the adsorption-desorption experiments, were perfomed to remove the
catalyst nanoparticles. Concentration measurements were again conducted by UV-vis
absorption spectrometry.
3.2.4. Wastewater treatment plant effluent
The influence of a chemical background and ultra-low concentration was examined to
test the model under more realistic circumstances. For this experiment, the effluent
of a wastewater treatment plant was used. The Stadtentwässerung Dresden GmbH
provided samples from the municipal plant in Kaditz (Fig. 3.2). In this plant 55 • 106m3
sewage water is treated per year. This treatment plant currently cleans the sewage
of 650000 people and has a design capacity of 740000 inhabitant equivalents. The
structure of the WWTP consists of a primary clarifier, an activated sludge reactor, and
a secondary clarifier [150]. Water was collected as a 24h flow proportional composite
effluent sample on June 24th, 2014, after two relative dry weeks (4.2 Lm−2) and stored
at 4 °C. Standard measurements of the effluent sample are summarized in Tab. 3.1.
All effluent samples were filtered by a filter paper (VWR pore sizes 5-13 µm) to remove
suspended particulate matter.
Figure 3.2.: Wastewater treatment plant in Kaditz operated by Stadtentwässerung
Dresden GmbH.
Besides the collected effluent sample, amixture ofMillipore water with carbamazepine
(12mgL−1) was created. From both samples 50mL were mixed with ZnO and TiO2
(1 g L−1) and exposed under continuous stirring to UV-radiation. The samples were
53
3. Materials and methodsfiltered and centrifuged as described previously. For the spiked sample, the measure-
ments were performed with the Varian CARY-100 UV-vis spectrophotometer. The un-
altered effluent sample was analyzed using SPE-HPLC-MS/MS.
Table 3.1.: Standard parametersmeasured in the effluent of thewastewater treatment
plant in Kaditz. Taken as 24h flow proportional composite effluent sample
on June 24th, 2014
chemical oxygen demand (COD) 37 mgL−1
biochemical oxygen demand (BOD) 4 mgL−1
Nitrogen
Ntotal 12.0 mgL−1
total Kjeldahl nitrogen (TKN) < 5.0 mgL−1
Nammonium 0.31mgL−1
Nnitrite 0.03mgL−1
Nnitrate 7.40mgL−1
Ninorganic 7.74mgL−1
Phosphor
Ptotal 0.86mgL−1
Nphosphate 0.56mgL−1
pH 7.5
The initial experiment was limited to one pharmaceutical molecule. Eventually, mul-
tiple drugs should be monitored at the same time in the next step. Target pharma-
ceuticals were preselected based on their prescription statistics. This selection of 55
molecules was based on a study by Gurke et al. [144]. For monitoring the degradation
process, the initial concentration (Ci) of the pharmaceuticals needs to be significantlyhigher than the corresponding detection limit. Therefore, we set the lower limit to be
Ci > 0.3µg L−1.After an initial analysis of the effluent sample, 14 pharmaceuticals were selected to
be monitored in the degradation experiment. Based on the initial concentration crite-
ria the anticonvulsants carbamazepine Ci = 1.29µg L−1, gabapentin Ci = 11.30µg L−1,lamotrigine Ci = 0.98µg L−1, and oxcarbazepine Ci = 0.63µg L−1, the antidepressant
venlafaxine Ci = 0.58µg L−1, the beta blockers bisoprolol Ci = 0.58µg L−1, celiprolol
Ci = 0.35µg L−1, and talinolol Ci = 0.43µg L−1, the lipid-lowering drug bezafibrate Ci =0.48µg L−1, the opioid analgesic tramadol Ci = 0.624µg L−1, as well as the angiotensinreceptor antagonists candesartan Ci = 1.30µg L−1, eprosartan Ci = 0.56µg L−1, irbesar-
54
3.2. Experimental investigationstan Ci = 1.50µg L−1, and valsartan Ci = 3.59µg L−1 were analysed in the degradation
experiment. The selected pharmaceuticals are listed with their corresponding lower
limit of quantification (LLoQ) in Tab. 3.2. It is essential to keep in mind that this data is
a mere snapshot because the concentration of micropollutants can significantly vary
in sewage samples based on a diverse range of parameters, for example, weather
conditions.
Table 3.2.: Selected pharmaceuticals from different drug classes to be monitored in
the degradation experiment. in themost left column the lower limit of quan-
tification (LLoQ) is listed.
analyte drug class provider LLoQ in ng L−1
Carbamazepine anticonvulsant Sigma 50
Gabapentin Pfizer 200
Lamotrigine Sigma 50
Oxcarbazepine Cerilliant 50
Venlafaxine antidepressant Wyeth 50
Bisoprolol Merck 50
Celiprolol beta blocker Oxprenolol 50
Talinolol LGC Standards 50
Bezafibrate lipid-lowering drug Sigma 50
Tramadol opioid analgesic Sigma 50
Candesartan AstraZeneca 50
Eprosartan angiotensin receptor Sigma 50
Irbesartan antagonist Sigma 50
Valsartan Sigma 100
As the SPE-HPLC-MS/MSmethodneeded significantlymore volumeper sample tomea-
sure all the concentrations, the sample volume was increased from 50mL to 100mL.
The treated wastewater were mixed with photocatalyst until a concentration of 1 g L−1
was reached. The altered setup lowered the UV intensity inside the bigger beakers to
15-16Wm−2 as determined by the UV34 LuxMeter (PCE). After the suspension was ex-
posed under continuous stirring to the UV-radiation aliquots of 2mL were withdrawn
at specific time intervals. Because the sample was analyzed by the SPE-HPLC-MS/MS
method, the filtering was skipped, and the samples were centrifuged for 60minutes to
remove the significant part of catalyst particles. As controls, the experiments were in
addition carried out in the absence of catalyst nanoparticles or without UV irradiation.
55
3. Materials and methodsAll other parameters in the control experiments were kept unchanged.
3.3. Modeling approach
This sectionwill focus on the theoreticalmodel of the degradation of organicmolecules
through photocatalysis. After describing the fundamental interactions in the system,
the model variants are described in detail. Beginning with the single-species model
and then continuing with the three alterations of the multi-species model. The pro-
cesses occurring during the photocatalytic degradation of organic components in the
solution are illustrated in Fig. 3.3. The steps towards complete mineralization of the
organic molecules is considered to take place mainly at the surface of the photocat-
alytic material. As radicals are extremely short-lived, the possible reactions of radicals
and organic compounds in the water surrounding the particle are neglected.
The organic components diffuse to the surface of the photocatalytic nanoparticles,
where they are adsorbed andmineralized. Organicmolecules desorb and diffuse away
from the particle at the same time, limiting the mineralization process. This process
is repeated for the fragments of the initial molecule until a complete mineralization
ist reached. For this modeling approach, it is presumed that the oxygen supply for
mineralization is sufficient during the entire process. This can be accomplished by
intense mixing in contact with the open atmosphere or with the help of a bubbler.
For the initial Gedankenexperiment, we are starting from a homogeneous solution of
the organic molecules. As soon as the photocatalytic material is added to the system,
the organic molecules start to be adsorbed at the nanoparticle surface. This adsorp-
tion results in a slight concentration gradient around the particles, depending on the
adsorption rate. However, the concentration profile strongly flattens in a brief mo-
ment due to the relatively fast diffusion of the organic molecules in the solution. In the
dark, without a reaction flow, the desorption and diffusion will finally lead again to a
homogeneous solution with a reduced concentration. When the reaction is initiated
through light, the mass-flow towards the surface will continue. To assess if diffusion
processes in the solution need to be taken into account, an estimation of the diffusion
speed of the model substance ciprofloxacin is done.
56
3.3. Modeling approach
jdes
jads
jreac
M
photocatalytic material initial molecules fragments
Figure 3.3.: Illustration of the processes occurring during the mineralization of organic
molecules at the surface of photocatalytic nanoparticles in solution. Due to
degradation and desorption, various intermediate organic molecules (frag-
ments) can emerge on the surface and in the solution. The degradation
steps on the surface create the final mineralized products (M).
D = kBT/(6π η r) (3.8)
By means of the Stokes-Einstein equation (Eq. 3.8) where η = 10−3 Pa s is the dynamicviscosity of water at 20 °C and r = 0.46nm is the radius of a sphere with a volume
equal to the van-der-Waals volume of ciprofloxacin (0.41 nm3), we find a diffusion co-
efficient of 4.65 • 10−10m2 s−1. A similar value of around 4.65 • 10−10m2 s−1 is obtained
when using the empirical equation presented by Wilke and Chang [151]. The order
of magnitude of the maximal diffusion distance between the nanoparticles, which the
molecules have to overcome, is given by a = C–1/3P
, where CP is the particle concen-tration. For a particle suspension of 1 g L−1 TiO2 and an upper estimate of the particle
radius of 50nm (considering possible agglomeration), one finds a ≈ 1300nm. This
results in a characteristic diffusion time tD = a2/D of 3.6ms [152]. Since this time is
57
3. Materials and methodsorders of magnitude smaller than the time, where significant mineralization of the or-
ganic molecules occurs, a homogeneous concentration of organic molecules between
the nanoparticles can be assumed in the following model approaches.
3.3.1. Single organic species model
The first modeling approach follows previous studies (see, for example, [45, 35] and
references therein) and consider an idealized model system with only one organic
species in the aqueous solution. Organic molecules in the solution adsorb onto the
particle and are mineralized due to photocatalytic reactions. The molecules can also
desorb before the mineralization. These three possible paths are shown in the reac-
tion equation below (Reac. 8).
A(aq) A(ad) M(aq) {8}
In the first part of the experiment that is performed in the dark, only the adsorption
and desorption plays a role. Temporal changes of the molecule concentration in the
solution CA(aq), in m−3, and the concentration on the photocatalyst particle surface
CA(ad), in m−2, are given by Eqs. 3.9 and 3.10.
d
dtCA(ad) = jads – jdes – jreac (3.9)
d
dtCA(aq) = as(jdes – jads) (3.10)
These equations include the specific surface area of the nanoparticles aS and the threedifferent molecule fluxes as shown in Eqs. 3.11-3.13.
jads = kads (1 – Θ)CA(aq) (3.11)
jdes = kdes CA(ad) (3.12)
jreac = kreac CA(ad) (3.13)
58
3.3. Modeling approachThe adsorption flux jads is proportional to the molecule concentration in the solutionand the free surface area of the particles. It is assumed that a monolayer is formed.
The surface coverage Θ is given by Eq. 3.14.
Θ = Am CA(ad) (3.14)
In this equation, Am is the surface area covered by one molecule. The largest possible
projection of the solvent-accessible surface is used to estimate this area [153]. For
this parameter, the van der Waals surface is probed by a molecule. To reduce the
resource demanded to generate such a surface, the solvent is abstracted as a sphere.
Most commonly, water is used as the probe molecule with a corresponding sphere
radius of r = 1.4 Å.
a) b) c)
Figure 3.4.: Steps to calculate the maximal projected accessible surface area of cipro-
floxacin: a) spatial structure generation, b) rotation and casting circles with
combined van der Waals and probe radius, and c) eroding with probe disk.
For this model, the full three-dimensional surface of the molecule is not needed, as
we are only interested in the maximal covered area. To efficiently calculate Am the
following steps are performed as depicted in Fig. 3.4. First, the spatial structure of the
organic molecule is gathered from a central repository like PubChem. For molecules
that are not yet included in a database, the 3D optimization can be done with the
MMFF94 force field [154]. Merck developed this force field with organic and drug-like
59
3. Materials and methodsmolecules in mind. Therefore, the list of supported elements is limited to the ones
typically needed for organic molecules (C, H, N, O, F, Si, P, S, Cl, Br, I). The 3D structure
of ciprofloxacin is shown as an example in Fig. 3.4 a.
In the second step, the principal axes of the molecule are determined based on the
atom positions. Knowing the principal axis enables the rotation of the molecule in
such a way that the maximal area is stretched out along the x and y-axis. Now the
problem is transformed into a two-dimensional system by omitting the z-axis informa-
tion. Centered on all atoms in the molecule circles are drawn with the corresponding
van da Waals radius combined with the probe radius (Fig. 3.4 b). The van der Waals
radii are taken from the 1964 publication by Bondi [155]. An exception is hydrogen,
which radius was found to be overestimated by 0.1 Å by Rowland and Taylor in 1996
[156]. All radii that are not listed in these publications are assigned the value of 2.0 Å.
However, these elements do not play a crucial role in organic molecules.
In the last step, the newly created area is eroded using a disk with the same radius
as the probe. The resulting area (Fig. 3.4 c) is used to determine Am. It is important tonote that the resulting value estimates the maximal surface area and can not express
the real adsorption geometries of organic molecules.
The reaction flux jreac describes the number of mineralized molecules per area and
time. Both desorption and reaction fluxes are proportional to the concentration of
organic molecules on the surface. In the limiting case of small surface coverage Θ � 1,
the system of ordinary differential equations, Eqs. 3.9 & 3.10, becomes linear and can
be solved analytically. The full derivation is presented in Appendix - chapter A, and the
solution is shown in Eqs. 3.15 and 3.16.
CA(aq)(t) = k1 exp(λ1 t) + k2 exp(λ2 t) (3.15)
CA(ad)(t) = k1λ1 + as kadsas kdes exp(λ1 t) + k2 λ2 + as kadsas kdes exp(λ2 t) (3.16)
The rate constants kads, kdes, and kreac are derived experimentally. First, the adsorptionand desorption rates are obtained from experiments of the concentration evolution
CA(aq)(t) in the dark. After an initial decrease of the concentration, a stationary value
is reached due to an adsorption-desorption equilibrium at the particle surface. For
sufficiently diluted concentrations, the emerging coverage on the particle surface is
minimal: Θ � 1. The concentration evolution results as solution of Eq. 3.9 with jreac =0 as
3. Materials and methodswhere the asymptotic surface concentration follows from the total particle balance as
CA(ad),∞ = 1
as (CA(aq),0 – CA(aq),∞). (3.20)
After determination of the rate constants kads and kdes by means of experiments con-ducted in the dark, the reaction rate constant kreac is determined from concentration
measurements obtained in the degradation experiments under illumination. During
the fitting procedure, Eqs. 3.9 and 3.10 are solved numerically.
For the case of a fast establishing adsorption-desorption equilibrium with a quasi-
stationary surface concentration CA(ad) = 0, the surface concentration in the system
of equations 3.9 and 3.10 can be eliminated. This would be the case when |CA(ad)| �kads CA(aq) or kdes CA(ad). The solution of Eq. 3.9 in the limit of small coverage Θ � 1
reads then CA(ad) = CA(aq) kads(kdes + kreac)–1. Insertion of this expression into Eq. 3.10yields CA(aq) = –kappCA(aq) with the solution
CA(aq)(t) = CA(aq),0 exp(–kappt) (3.21)
where the apparent degradation rate constant is given by
kapp = askadskreackdes + kreac . (3.22)
Thus, for kdes � kreac, we find kapp = askads. The degradation rate becomes adsorption-limited and does not depend on the reaction rate constant. In the opposite case,
kdes � kreac, one obtains kapp = askadskreac/kdes. The degradation rate is proportionalto the reaction rate constant.
62
3.3. Modeling approach
3.3.2. Multiple organic species model
The single organic species model is an appropriate tool for analyzing the adsorption-
desorption process of the initial organic compounds. However, photocatalytic miner-
alization of organic molecules is a far more complicated process, accompanied by the
formation of various intermediates in several reaction steps. Therefore, two idealized
mechanisms were considered to describe the mineralization reaction in more detail
(Fig. 3.5). In the first model, the initial organic molecule is oxidized step by step. It
can be imagined that in this model, the mineralization occurs just at the outer ends
of the initial molecule and its intermediates. Every time a reaction step happens, only
a small part (e.g. one carbon atom) is oxidized. This model is thus referred to as the
incremental oxidation model.In the second model, referred to as fragmentation model, it is considered that bondswithin the molecule are destroyed due to photocatalytic reactions. In contrast to the
first model, molecules can now break into two smaller fragments without mineraliza-
tion.
Based on the secondmechanism, themodel is extended further. As the initialmolecule
and the intermediates are portrayed as a chain, information from the original molecule
is lost. Through the introduction of excess bonds, the backbone of the base moleculecan be better captured. A reaction step can reduce these excess bonds in the same
way the fragments are broken apart.
Intermediates may desorb from the catalyst surface instead of further undergoing di-
rect reactions in all models. Thus concentrations of different species need to be intro-
duced in the solution and on the surface of the catalyst. The different species will be
characterized solely by their size.
Incremental oxidation model
The initial organic compounds and their intermediates are described by the number of
carbon atoms n in their structure to build a model that incorporates different species.Within the incremental oxidation model, the molecule degradation is described in an
idealized manner by oxidation and removal of one carbon atom at every reaction step
(see Fig. 3.5). With the separation of each carbon atom, a corresponding fraction of
the remaining molecule is considered mineralized. Adsorption, desorption, and min-
63
3. Materials and methods
C +
+
+
+
C C C C C
C C C C
C C C C C
C
C C
C C
C C C
C C
C C C C
C
C C
C C
C
M
M
M
M M
+
+
+
+
+
C C C C C C C
C C C C C C C
C C C C C C C
C C C C
C C C C
+
+
C C C
C C
C C C C
C
C C
C C
C
C C C
C C C
C C
M
C C
M
C C
. . .
. . .
fragmentation
incremental
Figure 3.5.: Illustration of the reaction steps in the two basic multiple organic species
models: (top) incremental oxidation and removal of single carbon atoms
and (bottom) formation of fragments of molecules by intermolecular bond
breaking and subsequent oxidation of the smallest fragments.
eralization of a molecule of size n can, therefore, be expressed by Reac. 9.
An (aq) An (ad) A(n–1) (ad) + M(aq) {9}
The concentration evolution of molecules of size n ≥ 2 and of the mineralized compo-
3.3. Modeling approachThe corresponding fluxes are defined in Eqs. 3.26-3.28.
jn,ads = kn,ads (1 – Θ)CAn(aq) (3.26)
jn,des = kn,des CAn(ad) (3.27)
jn,reac = kn,reac CAn(ad) (3.28)
The flux j(n+1),reac in Eq. 3.23 describes the formation of molecules of size n due to
oxidation of molecules of size n + 1. To track the concentration of the mineralized
component CM in the solution, the mineralization fluxes of all molecules is summed as
shown in Eq. 3.25. For simplicity, we assume the rate constants in Eqs. 3.29-3.31 to
vary only with the molecule size n.
kn,ads = κDn (3.29)
kn,des = ν0(n) exp(–Edes(n)kB T
)(3.30)
kn,reac = I0 φ An (3.31)
It is reasonable to assume that the size of the fragments considerably affect the rate
constants. Especially, for chain like molecules with equal repeating units. In general,
the rate constants depend also on the specific element composition and configuration
of the molecules. Roughly, we choose the adsorption rate constant to be proportional
to the diffusion constant of the molecules, which in turn is determined by their size
according to the Stokes-Einstein equation (Eq. 3.8). The molar volume, used to esti-
mate the spherical molecule radius, is supposed to be proportional to the number
of carbon atoms n. Dividing the initial molecule volume up for the intermediates willunderestimate their values. The reaction rate constant is chosen to be proportional
to the area of the photocatalyst surface covered by the molecule. This choice arises
from the idea that the reactions can happen with a constant probability over the en-
tire catalyst surface. If an intermediate covers more of this surface, it is more likely to
encounter a reaction in the same time frame. The remaining constants κ, and φ in Eqs.3.29-3.31 are chosen to match the experimentally found rate constants of the initial
molecule. Little is known about the dependence of the desorption rate constant on
65
3. Materials and methodsthe molecule size for aqueous solutions. For the desorption of organic molecules in
vacuum, temperature programmed desorption studies [157] and molecular dynamics
simulations [158] have been performed. For example, for the desorption of alkanes
CnH2n+2 from the MgO(100) surface, experimental investigations in [157] showed the
desorption energy Edes to depend linearly on the chain length n.
Edes(n) = (6.5 + 7.1n) kJmol–1 (3.32)
The pre-exponential factor ν0 strongly increased in the same setup from 1013.1 to
1019.1 for n varying from 1 to 10. To what extent similar tendencies apply to desorp-
tion in aqueous solutions is not known. We consider, as one assumption in this model,
that similar behavior occurs, where the desorption energy and pre-exponential factor
depend on the molecule size in the following way.
Edes(n) = E0 + E1 n (3.33)
ν0(n) = α0 10α1n (3.34)
The parameters in these equations were chosen so that the desorption rate agrees
with the rate derived fromexperiments in the darkwith the initial organicmolecules. As
a consequence of such a strong size dependence, small intermediate molecules exhibithigh desorption rates, leading to a low mineralization rate of these components. As
demonstrated later in the section 4.3.2 (p. 83), this results in a prolonged decay of the
total organic carbon (TOC) signal even after extended exposure time. Such residual
long-term TOC signals have been reported in [159, 160, 161, 162].
The desorption rate of intermediates depends, of course, not only on themolecule size
but crucially on their chemical structure as well. The TOC signal in many degradation
studies has been observed to vanish entirely after moderate illumination exposure
[163]. For this reason, we consider the case of weak size dependence of the desorptionrate of intermediates.
66
3.3. Modeling approach
kn,des = β0 + β1/n (3.35)
As a possible model function for this size dependence, we have chosen a simple rela-
tionship with only two parameters. The simplicity of the relationship in equation 3.35
facilitates parameter fits from experimental data.
Fragmentation model
In this model, we consider the limiting case that photocatalytic reactions lead to the
progressive destruction of bonds in the molecules on the catalyst surface (Fig. 3.5).
Only the smallest possible fragments are considered mineralized. The initial molecule
is abstracted as a chain, where the number of possible fragmentations of a molecule
of size n is equal to n-1. The corresponding reaction equations for the species An isgiven in Reac. 10.
The corresponding fluxes are defined in Eqs. 3.44-3.46.
jn,β,ads = kn,ads (1 – Θ)CAnEβ(aq) (3.44)
jn,β,des = kn,des CAnEβ(ad) (3.45)
jn,β,reac = kn,reac CAnEβ(ad) (3.46)
In Fig. 3.7 all possible fragments for ciprofloxacin and an exemplary reaction pathway
are shown. As in the previous model variant, multiple reaction pathways are possible
for each adsorbed molecule. In addition to the inflow from larger molecules, a new
pathway is added from a fragment with the same size n but with one additional exces-sive bond. The following sum can represent the incoming reaction flux j∗n,b,reac for thissystem.
j∗n,β,reac = nmax∑m=n+1
[2(m–1)–b(m–1)2 km,reac CAm,b(ad)
]+
β+1n–1 kn,reac CAn,β+1(ad) (3.47)
The first part of the equation captures all reactions that yield AnEβ from larger mole-
cules (AnEβ (ad) AmEb (ad) + X). As these reactions have a lower priority, their overallprobability is defined by the ratio of free links (m-1-b) to all chain links (m-1). In the
same way, as described in the fragmentation model, each free link is equally probable
to be broken. Therefore, the same factor of 2/(m – 1) is introduced.
In the second part of the equation, the destruction of an excess bond is taken into
account. Here the probability is (β + 1)/(n – 1). For fragments that are on the left edgeof Fig. 3.7 the probability would be higher than one. A particle with β ≥ n cannot
be formed, as fragments with n = b + 1 can only lose an excess bond. This limitation
71
3. Materials and methodsaddresses the problem of the corner cases as all concentrations where β ≥ n are zero.
3.4. Model implementation
3.4.1. Development objectives
In the previous sections, the theoretical frameworks for the different models were laid
out. As the proposed models cannot be applied to experimental measurements in a
simple way, it is necessary to make an efficient implementation of them available. In
the following paragraphs, this implementation will be discussed.
The goal was to develop a reliable tool that is quickly accessible by experimentalists
as well as reusable for specific cases or new models. To make the software available
on the predominantly used operation systems, Python [165] was chosen as the pro-
gramming language. The quick prototyping capabilities of Python is beneficial during
development. The selection of Python enables an easy route to augment the core
implementation on the fly. Therefore, the user can change the operation of the code
if desired. The toolkit is released under the MIT license8 to facilitate the idea of open
science and incremental improvements through a wider community. This license is
very permissive and requires only the preservation of the copyright and license note.
Derivatives of the software are allowed to be published under different terms in the
future.
While the core library of Python already provides an extensive collection of modules,
it is not feasible to implement the full models in vanilla Python. Therefore, a few ex-
ternal libraries are included that enable practical scientific work under Python. For the
described models, packages from the SciPy ecosystem [166] are used. These are:
• the SciPy core library providing numerical routines,
• NumPy [167] defining new types for arrays and matrices,
• and Matplotlib [168] to render the simulation results.
To prepare the molecule data, scikit-image [169] is used to ascertain the occupied
surface area.
8The full license is available under https://github.com/theia-dev/pdom/blob/master/LICENSE.txt
72
3.4. Model implementationAs the toolkit should be reliable, and external contributions are encouraged, a system
for quality control is needed. For this propose a test-suite was put into practice, to
detect the impact of code changes on the simulation result. As of the time of writing,
16 different tests with 37 individual test-cases are implemented. These tests cover
94% of the core model source code.
The simulations can be started without the user needing to write Python code. This is
archived through the inclusion of two command-line tools. The first one pdom.config
helps to create configuration files. With the configuration file in place, pdom can then
run the simulation and stores the raw results and plots in the file system. Basing the
simulations on configuration files helps to ensure that the results of a simulation can
always be traced back by the parameters that created them.
3.4.2. Molecule parameters
For the simulation, multiple parameters describing the initial molecule are needed.
This data is collected from a central database to simplify the creation of the configu-
ration files. For this project, PubChem was selected. PubChem is an open chemistry
database provided by theNIH9. The required information is collected via an application
programming interface directly from the server.
Two parameters cannot be gathered directly from PubChem for the simulations, the
maximal projected accessible surface, and the excess bond count. The surface area
is calculated based on the 3D structure provided by PubChem. Tools provided by
scikit-image are used to implement the steps described in Sec. 3.3.1 (p. 58). The
backbone bonds in a molecule are counted based on the same structure information
provided by PubChem in an SDF file format. Through the comparison of the backbone
bond count and the number of carbon atoms in the molecule, the excess bond count
is determined.
3.4.3. Solving the differential equation system
The evolution of the concentrations C in the different models is presented as a simpli-fied differential equation.
9National Institutes of Health - USA
73
3. Materials and methods
∂C∂t = f (t,C, · · · ) (3.48)
The right-hand side (RHS) of Eq. 3.48 is implemented based on the different fluxes
described in the previous section. As an example, we can look at the implementation
of the RHS for the single-species model. The function rhs_single10 is called with the
current simulation time t, the number ofmolecules on the surface N[0] and in solution
N[1], and finally the simulation constants k. As none of the fluxes are dependent
on external time coupled fields, the current simulation time t is not utilized in the
calculation of the overall fluxes F.
1 def rhs_single(self, t, N, k):2 ka, kd, kr = k3 # Create empty array for the absolute flux per element4 F = np.zeros(2)5 # Calculate the surface concentration6 C_AS = N[0] / self.cfg['CATALYST']['surface_total']7 # Calculate the volume concentration8 C_A = N[1] / self.cfg['CATALYST']['volume']9 theta = C_AS * self.cfg['MOLECULE']['molar_surface']10 # Calculate the fluxes11 J_ads = C_A * (1.0 - theta) * ka12 J_des = C_AS * kd13 J_reac = C_AS * kr14 F[0] = (-J_des + J_ads - J_reac) * self.cfg['CATALYST']['surface_total']15 F[1] = (+J_des - J_ads) * self.cfg['CATALYST']['surface_total']16 return F
The overall number of molecules is used to ensure that the order of magnitude is
roughly similar for the complete system. This uniformity supports the work of the
solver as the relative, and absolute tolerances can be the same for the whole system.
Furthermore, it simplifies the definition of the overall flux F significantly. As the fluxes
are defined based on the concentration, the molecule count needs to be converted
in lines 6 and 8. The information regarding the surface area or volume is collected in
the central simulation config self.cfg. In line number 9, the coverage of the surface
is determined. After these preparations, the three fluxes can be calculated according
to Eq. 3.11 in lines 11-13. The overall change is then summed up in lines 14 and 15.
10docstring of the original function is omitted
74
3.4. Model implementationThe LSODA subroutine from the FORTRAN ODEPACK library is used to solve these equa-
tions. The LSODA routine is a derivative of the Livermore Solver for Ordinary Differential
Equations (LSODE). It was developed byHindmarsh and Petzold [170, 171] in 1983with
the capability to switch automatically between a nonstiff and stiff solver depending on
the behavior of the problem. For the nonstiff part of a problem, an Adams predictor-
corrector method is used. The stiff parts of a problem are handled by a Backward
Differentiation Formula (BDF) method. The nonstiff method is used initially to solve
the equation system. During the calculation, LSODA can switch dynamically between
the stiff, and the nonstiff method as necessary. For this project, the solve_ivp wrap-
per for LSODA from the SciPy library was used.
3.4.4. Fit to experimental results
Single organic species model
The proposed model cannot be analytically solved in a general way. This restriction
presents a challenge for the fit of experimental data to the models. As the calculation
of the single-species model is rather quick, we can use a custom error function. This
error function allows the selection of different error representations. In the tool are
three different types available: absolute, relative, and relative-squared. The users can
switch between them depending on their datasets.
The minimization workload is handled by Brent’s algorithm for finding a minimum of
a function of one variable [172, 173]. Brent’s method is based on a reliable golden
section search. Depending on the behavior of the function, an inverse parabolic in-
terpolation is used to jump closer to the minima. A different starting interval for the
downhill bracket search is selected for the different available fitting parameters, to
reduce the number of iterations.
Multiple organic species model
The development of the fragments produced by the photocatalytic reaction can be
measured through NPOC or TOC. The concentrations of the segments need to be
summed up to compare the model behavior to the experimental data. The contribu-
tion of a segment An to the total carbon footprint is determined by its carbon-count n.
75
3. Materials and methodsThis results in the following estimation of the TOC:
TOC = 12.0107 gmol–1
NAvo ·∑nmaxn=2 n ·
(NAn(aq) + NAn(ad))V (3.49)
This formula describes the development of the TOC for the whole system. Based on
the experimental setup, it might be appropriate to include only organic fragments in
solution. The user can set this behaviour in the configuration. As this method is an
estimation, it cannot precisely match the initial concentration of the start molecule
with the initial value measured for TOC/NPOC. To enable an efficient fit, the values are
scaled by the initial TOC value. This scaling results in a co-domain from zero to one for
the experimental and simulation data, which is in addition advantageous to the solver.
A damped least-squares method is used to fit the models to the TOC measurements,
specifically, the Levenberg-Marquardt algorithm for its efficiency. While first described
in 1944 by Levenberg [174] it was mostly forgotten, until it was made popular through
the implementation in FORTRAN by Marquardt in 1963 [175]. As the multi-species
models need significantly more computational time compared to the single-species
model, it is essential that the optimization requires as few function evaluations as pos-
sible. SciPy provides a wrapper around the FORTRAN implementation of this algorithm
from MINPACK following Moré’s proposals [176]. An excellent overview regarding the
Levenberg-Marquardt algorithm is provided by Pujol [177].
3.4.5. Availability
The source code for this implementation is available on the CD accompanying this
thesis. Additionally, the same version of the software is archived in the on the open
data platform zenodo under the DOI: 10.5281/zenodo.3953797. The latest source
code is available on GitHub11. Releases of the software are shared on the Python
Package Index12 (PyPI) for easy installation. The handbook belonging to the submitted
version can be found in Appendix - chapter C (p. 105). It describes the usage of the
tool in greater detail and providesmultiple examples. The documentation for the latest
version is available on the Read the Docs platform13.
The photocatalysts TiO2 and ZnO were characterized to gain an in-depth understand-
ing of their properties and extract relevant parameters for the simulation. For both
powders an SEM image at the same scale is shown in Fig. 4.1. TiO2 particles show a
more delicate structure compared to the ones in the ZnO sample. While the TiO2 pow-
der is composed of monodisperse nanospheres, the ZnO powder presents a more
complex polydisperse rectangular structures.
1.5µm
TiO2 ZnO
10 kV, 5mm, x50000 25 kV, 9mm, x50000
Figure 4.1.: SEM images of colloidal titanium dioxide (TiO2) and zinc oxide (ZnO).
The qualitatively observed differences in the SEM images are directly linked to themea-
77
4. Results and discussionsured specific surface area. This value is derived from BET measurements and used
directly in the calculations. For the P25 TiO2 nanopowder, a value of 56.0m2 g−1 in
agreement with reported data [178] was obtained. In contrast, the surface area of
ZnO was found to be approximately 1/10th at 5.23m2 g−1.
0
20
40
60
80
100
Lightintensity(E365nm
=100) Lamp
TiO2ZnO
436 405 365 313
min
max
Wavelength λ (nm)
Absorbance
Figure 4.2.: Light output of the used mercury fluorescent tubes normalized at 365nm
compared to the diffuse reflectance spectra of TiO2 and ZnO.
The UV-vis diffuse reflectance spectra of ZnO and TiO2 are presented in Fig. 4.2. In ad-
dition, the emission spectrum of the radiation device is provided. It can be observed
that ZnO absorbance already reached its highest level at 365nm. In contrast, the ab-
sorption potential of TiO2 reaches its maxima at higher energies around 310nm. In
general, a smaller difference between the two materials is expected. Due to the small
grain size of the TiO2 powder, its peak is shifted to shorter wavelengths. The lesser
incline of TiO2 is caused by the mixture of different crystal structures in the powder.
The transition between absorbing and non-absorbing is smoothed out by the different
bandgaps. Overall it indicates that the ZnO powder can utilize the light source more
efficiently.
78
4.2. Adsorption-desorption
4.2. Adsorption-desorption
The adsorption rate constants kads were first determined from concentrationmeasure-
ments performed in the dark. The corresponding values, calculated by using Eq. 3.18,
are listed in Tab. 4.1. These values have the same order of magnitude as reported in
[179]. From the asymptotic concentration values measured at adsorption-desorption
equilibrium, CA(aq),∞, the desorption rate constants were determined by the use of
Eqs. 3.19 and 3.20 (cf. Tab. 4.1).
Table 4.1.: Adsorption and desorption rate constants derived from experiments in the
dark for the compounds ciprofloxacin (CIP) and methylene blue (MB) using
photocatalysts TiO2 and ZnO, respectively.
system kads in m s−1 kdes in s−1TiO2-CIP 3.7 • 10−8 2.05 • 10−2
TiO2-MB∗ 2.1 • 10−8 2.85 • 10−2
ZnO-CIP 7.5 • 10−7 9.4 • 10−3
ZnO-MB 5.4 • 10−7 9.3 • 10−3
∗ Fit from degradation experiment
An exception, in the data shown in Tab. 4.1, is the combination of methylene blue with
TiO2. To demonstrate a different approach, the adsorption constant kads was fitted inthis case to data collected under UV light and not in the dark. As shown in the next
section, is the used setup limited by the adsorption speed of the organic molecule.
Therefore, the degradation curve recorded in the experiment is just defined through
the adsorption and desorption constants. In combination with the concentration drop
from the equilibrium phase before the degradation experiment, both parameters can
be determined. On the one hand, this approach makes it possible to reduce the time
investment by eliminating the need for multiple dark experiments. On the other hand,
it is not possible to make a detailed statement about the reaction constant in this case.
The data show that the adsorption rate of methylene blue on ZnO and TiO2 is lower
than that of ciprofloxacin. Comparing the two catalysts, one finds that adsorption on
ZnO is about 20 times faster than on TiO2. This faster adsorption demonstrates that
ZnO presents a more attractive surface for the tested organic molecules compared to
TiO2.
A third approach to extract the adsorption constant kads, is to fit a full time-series of
79
4. Results and discussiondark experiments. In the publication by House et al. [159], their experiments in the
dark are portrayed in rich detail. When the adsorption of a system is as slow as in
this case, determining variations in the concentration close to t = 0 can be challenging.Fitting the experimental data to the single-species model (cf. 3.4.4, p. 75) with the re-
action flux turned off can be used to extract the adsorption and desorption constant
in such a case (Fig. 4.3).
0 0.5 1 1.5 2 2.5 3 3.5 40
5
10
15
20
25
time t (h)
surfa
ceconcentrationC A
(ad)(g/m
2 )
30mg/L 25mg/L15mg/L 5mg/L
Figure 4.3.: Simulation results for the adsoprtion/desorption dynamic of methylene
blue (MB) on TiO2 based on data reported in [159] (as=1.4 • 105m−1). The
marks show the experimental results for the different initial concentra-
tions of MB (5, 15, 25 and 30mg/L). The full line is a fit according to the
single organic species model without reaction flux. The resulting parame-
ters (kads=9.37 • 10−10ms−1, kdes=1.10 • 10−3 s−1) are the same for all four
curves.
While the adsorption constant is over a magnitude smaller kads = 9.78 • 10−10ms−1
compared to the setup used in the experiments presented in this work, the ratio to
the desorption constant kdes = 1.15 • 10−3ms−1 is similar. Differences in the adsorption
value could be due to different pH values of the solutions. For low concentrations (Θ� 1) it follows from Eq. 3.19 that the ratio between the constants is approximately
the same as between the concentration in the solvent and the concentration on the
catalyst surface after the equilibrium is reached (Eq. 4.1).
80
4.3. Photocatalytic degradation
kdeskads ≈CA(aq),∞CA(ad),∞ (4.1)
4.3. Photocatalytic degradation
4.3.1. Single organic species model
The results of the degradation experiments under UV-irradiation are shown in Fig. 4.4.
To fit the measured data points within the framework of the single organic species
model, the adsorption rate constants derived from the experiments conducted in the
dark (Tab. 4.1). The fitting procedure revealed that all values for the reaction rate con-
stant above a certain threshold fit the measured data points. From this observation,
it can be concluded that the adsorption of organic compounds was rate-determining
and that the reaction rate constant is higher than the desorption rate constant (cf. dis-
cussion at the end of Sec. 3.4.4, p. 62). As stated above, the adsorption rate constant
for the system TiO2-methylene blue kads was fitted to the degradation curve, assumingadsorption to be rate-determining.
Further experiments (Fig. 4.5 a) with one half of the TiO2 particle concentration re-
vealed that the degradation of ciprofloxacin slows down. The degradation half-life time
was changed by a factor of 2.05, close to the expected value 2. This corresponds to
themodel prediction in Eq. 3.22 where the rate constant is proportional to the specific
particle surface as. Measurements of the ciprofloxacin concentration for degradationon TiO2 with reduced UV-irradiation are shown in Fig. 4.5 b. Remarkably, the curve
fit yields a reaction rate constant kreac = 0.01 s−1, which is one half of the desorptionrate constant. According to the expression for the apparent rate constant Eq. 3.22,
this means that at this irradiation intensity and below, the degradation rate becomes
reaction-limited.
The slight disagreement between the fitted exponential curve in Fig. 4.5 b and themea-
surement data reflect the limits of the single organic species model. Development
and adsorption of intermediates could modify the degradation curve of ciprofloxacin.
Especially when the reaction speed is the limiting factor, the influence of adsorbed
intermediates plays a more significant role.
81
4. Results and discussion
0
2
4
6
ConcentrationC A
(aq)(102
1m
–3)
simulationexperiment 1experiment 2
0 5 10 15 20 250
2
4
6
Time t (min)0 5 10 15
TiO2 ZnO
ciprofloxacin
methylene
blue
a)
c)
b)
d)
Figure 4.4.: Measured concentration evolutions during the degradation of ciprofloxa-
cin (a,b) and methylene blue (c,d) under UV-irradiation with 1.0 g L−1 cata-
lysts TiO2 (a,c) and ZnO (b,d). The full lines represent fits according to the
above single organic species model using the values of kads and kdes deter-mined from experiments in the dark (Tab. 4.1). The dotted line in panel c)
was obtained by fitting kads from the degradation curve, assuming adsorp-
tion to be rate-determining.
82
4.3. Photocatalytic degradation
0 5 10 15 20 250
2
4
6
8
Time t (min)
ConcentrationC A
(aq)(102
1m
–3)
simulationexperiment 1experiment 2
0 5 10 15 20 25
concentration TiO2 0.5 g L–1 UV intensity 5.5Wm–2
ciprofloxacin
a) b)
Figure 4.5.: Measured concentration evolutions during degradation of ciprofloxacin
with TiO2. Compared to Fig. 4.4 a), a reduced TiO2 particle concentration of
0.5 g L−1 a), and a lower UV-irradiation of 5.5Wm−2 b) was used. The lines
represent fits according to the single organic species model using the val-
ues of kads and kdes determined from the dark experiments (Tab. 4.1). The
fitted reaction constant in panel b) is kreac=0.01 s−1.
4.3.2. Multi organic species model
The concentration evolution of the initial organic compound can be well described by
an exponential decay exp(–kappt) with kapp as the apparent degradation rate constant[159, 161, 162, 179] (cf. Eq. 3.21). Measurements of the evolution of the TOC in the
solution often show an exponential-like decay as well. There are, however, studies
where the TOC does not exhibit such behavior [159, 160, 161, 162]. This mismatch is
likely related to the mineralization kinetics of the intermediate organic compounds. To
demonstrate such complex degradation kinetics of the intermediates, Fig. 4.6 shows
the calculated concentration evolutions of all intermediates based on the the different
variations of the multi organic species model (cf. Sec. 3.4.4, p. 75).
In Figures 4.6 a, c and e, the case of a weak dependence of the desorption rates of
intermediates on the molecule size n is considered (cf. Eq. 3.35). For the incremen-
tal oxidation model (Fig. 4.6 a) as well as for the fragmentation model (Fig. 4.6 c), all
intermediates are mineralized within moderate irradiation time. The excess bonds
model (Fig. 4.6 e) takes the most time of all three models. The smallest intermediate
needs the longest time since its desorption rate is the highest. For the incremental
83
4. Results and discussion
0
1
2
3
4
234
234
0
5
10
15
20
25
234
ConcentrationC A
(aq)(102
1m
–3)
234
0 1 2 3 40
5
10
15
20
25
234
Time t (h)0 1 2 3 4
234
a)
c)
e)
b)
d)
f)
weak strong
increm
ental
fragm
entation
excessbonds
Figure 4.6.: Calculated concentration evolutions of ciprofloxacin intermediates of sizen (curve labels) based on the incremental (a,b), fragmentation (c,d) or ex-
cess bond (e,f) oxidation model with weak (a,c,e) or strong (b,d,f) depen-
dence of the desorption rate constants on the molecule size n accord-
ing to Eqs. 3.33 to 3.35. Parameters: nmax=17, bmax=11, Am=1.028nm2,as=5.6 • 104m−1, kads=3.7 • 10−8ms−1, kdes=2.05 • 10−2 s−1, kreac=0.4 s−1;weak: β1=0.8 s−1; strong: E1=3.0 kJmol−1, E0=44.0 kJmol−1, α1=0.412.
84
4.3. Photocatalytic degradationoxidation model, small intermediates emerge with some delay, whereas in the other
two models, all compounds are produced with similar initial rates. Besides, for the
latter models, particularly high concentrations of small intermediates arise, which are
formed by fragmentation of all larger intermediates, this is contrary to the incremen-
tal oxidation mechanism. As the fragmentation and excess bond models are closely
related, the main difference is the shift of the peaks to later points in time. This shift is
caused by the additional reaction cycles necessary to destroy the excess bonds.
The concentration curves in Figures 4.6 b, d and f show the effect of a strong increase
of the desorption rate of intermediates with decreasing molecule size (cf. Eq. 3.34). An
inhibition of a quick and completemineralization of organic compounds in the solution
is the result. Smaller intermediates remain intact even during long irradiation times.
Due to their high desorption rate their surface coverage is minimal. Possibly, these
small intermediates could be oxidized to a noticeable extent by radicals in the aqueous
solution. This reaction path was, however, neglected in the present model.
The characteristic concentration evolutions in Fig. 4.6 are comparable to experimental
measurements. For example, the plots in Fig. 4.6 c are similar to the evolution of cer-
tain intermediates during photocatalytic degradation of sulfamethoxazole observed
in [37]. In the case of the intensively studied degradation of phenol [180, 181], the
intermediate concentrations show a similar form as well. The evolution of reaction in-
termediates has further been explored for the gas phase oxidation of decane [182].
Many intermediates show concentration evolutions similar to Fig. 4.6 c. However, there
are few crossings of concentration profiles, as seen in Fig. 4.6 b as well.
A detailed view of the excess bond development is presented in Fig. 4.7. This figure
corresponds to the development of the concentration of the intermediates in Fig. 4.6 e.
It shows that while the average number of excess bonds for a given fragment size ndeclines, the overall excess bonds are degraded over the full range of intermediates.
This behavior is a result of the modeling decision to assume that excess bonds are not
specifically targeted.
Measuring the concentration evolution of intermediates directly during an experiment
is quite challenging. To still access information about the intermediates, the overall
amount of organic compounds that remain in the solution can be monitored through-
out the degradation experiment. This value is commonly characterized by measuring
the TOC often in the form of the non-purgable organic carbon (NPOC) (Sec. 3.1.4, p. 49).
85
4. Results and discussion
0 1 2 3 40
2
4
6
8
10
12
17
16
15
Time t (h)
Averagenumbero
fexcessbonds
0
20
40
60
80
100
Overalle
xcessbonds(%)
Figure 4.7.: Change in the overall excess bonds and average number of excess bonds
for intermediates of size n (curve labels). Parameters are choosen as in Fig.4.6 for a weak size dependence of the desorption rate. The curves for the
average number of excess bonds are limited to regions with a concentra-
tions of at least 10m−3 for the corresponding intermediates.
For this reason, we have calculated the evolution of the TOC within this proposedmod-
els. Fig. 4.8 displays the characteristic differences of the TOC evolution between the
three splitting mechanisms discussed above. On the left side, the effect of equalizing
the system in the dark can be perceived. As the adsorption and desorption fluxes are
in equilibrium, the surface is covered with many molecules at the start. Initially, the
degradation process is rate limited by the reaction constants. The intermediates cre-
ated in this phase are still located on the surface. After a few seconds, the surface
concentrations are lowered significantly, so that most reactions are no longer limited
by the reaction rate constant, but through the influx of molecules from the solution.
For the excess bond model, a significant part of the occurring reactions do not con-
tribute to a reduction of the TOC in the beginning but reduce the overall number of
excess bonds. This depletion of reaction potential results in a slower start compared
to the other models. Due to the small-time scale, it is unlikely that this effect can be
captured in an experimental setup.
The right part of Fig. 4.8 is more relevant for comparisons to experimental findings. For
86
4.3. Photocatalytic degradation
0 2 4
3.1
3.2
3.3
3.4Totalorganiccarbon
TOC(mgL
–1)
0 60 120 180 240 0
0.5
1
1.5
2
2.5
3
3.5
Time t (min)
incrementalfragmentexcess bondsweakstrong
Figure 4.8.: Comparison between the TOC evolution for the incremental, the fragmen-
tation, and the excess bonds oxidation model for weak and strong size
dependence of the desorption rate. Parameters are choosen as in Fig. 4.6.
weak size dependence of the desorption rate of intermediates, the incremental oxida-
tion mechanism under moderate irradiation shows an exponential-like decay of the
TOC signal as the organic material disappears. For the fragmentation mechanism and
weak size dependence of the desorption rates of intermediates, the TOC curve shows
an inflection point at the beginning (at about 10min). This slight initial delay in the TOC
signal reduction is caused by the fact that only the smallest fragments are mineralized.
Their formation needs a certain amount of time. Using the excess bonds model, this
inflection point is found later (at around 30min) when the split of a fragment becomes
more likely compared to the removal of an excess bond. At this point in time around
50% of the initial excess bonds are degraded (see Fig. 4.7).
In the case of the incremental degradation mechanism and strong size dependence
of the desorption rate, the TOC signal shows still a fast initial decrease followed by
a considerably slower decay, whereas the fragmentation mechanism shows a more
gradual initial decrease. After a very slow initial phase until around 90min, the degra-
dation rate of the excess bond model increases slightly. An exponential-like tail region
follows this part. For all degradation mechanisms with strong size dependence of the
87
4. Results and discussiondesorption rate, the high desorption constants limit the number of small intermedi-
ates that stay adsorbed on the surface. Therefore, following Eqs. 3.28 and 3.39, these
intermediates will be degradeted slowly. It can be expected that a certain amount of
small organic compounds remains even after a reasonable long irradiation exposure.
Figure 4.9.: Simulation results for the degradation of methylene blue by TiO2 based
on data reported in [159] (as=1.4 • 105m−1). The full line is a fit ac-
cording to the single organic species model. The resulting parameters
(kads=3.0 • 10−9ms−1, kdes=6.8 • 10−3 s−1) were used for fitting the TOC
curves. For the reaction constant kreac=10 kdes was chosen. The desorp-tion behavior of the intermediates was modeled by Eq. 3.35 with nmax=16(fragmentation model: β0=−6.57 • 10−3 s−1, β1=0.122 s−1; incremental oxi-dation model: β0=−3.06 • 10−2 s−1, β1=0.496 s−1).
Houas et al. [159] studied the degradation of methylene blue on TiO2 and the corre-
sponding TOC evolution. From the presented adsorption experiments, we extracted
the adsorption and desorption rate constants as discussed before (Sec. 4.2, p. 79).
While fitting the degradation curve in preparation with the single-species model, it was
found that the adsorption constant extracted from the experiments in the dark was
to low to explain the presented curve. This analysis suggested that the degradation is
adsorption-limited, i.e. kreac is considerably larger than kdes. Thus, kreac = 10 kreac waschosen in the simulations. The adsorption constants extracted from the degradation
curve under this condition was kads = 3.0 • 10−9ms−1 and while larger than the value
88
4.4. Wastewater treatment plant effluentobtained in the dark it is still in the same order of magnitude. The corresponding des-
orption constant was determined from the equilibrium concentration as shown in Fig.
4.3 as kdes = 6.8 • 10−3 s−1.
Fig. 4.9 shows the simulation results for the TOC data in [159] obtainedwithin the incre-
mental oxidation and fragmentation models and using Eq. 3.35 for the description of
the desorption behavior of intermediates. The number of intermediates was chosen
as the number of carbon atoms inmethylene blue (nmax = 16). Comparison of the fittedTOC curves in Fig. 4.9 with the experimental data shows that both models fit different
stages of the degradation. The long-term evolution is better fitted by the incremental
oxidation model. In the initial phase, the assumption that all connections between in
the abstracted organic molecule components have the same probability of breaking
could be the problem in this case. The delay in the TOC reduction can be explained
with the existence of a preferred breaking point closer to the center of the virtual
molecule. This preference would delay the production of materialized components in
the beginning. Additionally, the approximated adsorption-desorption properties could
be different for specific intermediates. Clearly, for a more detailed quantitative under-
standing of TOC measurements as well as of the evolution of intermediates, a deeper
knowledge of species-specific adsorption-desorption is needed. The incorporation of
a specific reaction tree would prevent the model from being applied universally.
4.4. Wastewater treatment plant effluent
4.4.1. Influence of effluent
The effluent of aWWTP represents a challengingmatrix for photocatalytic degradation.
Due to different parameters like ion concentration, pH value, or the diverse mixture of
organic and inorganicmolecules the concentration development overtimemight differ
from a clean laboratory experiment. To examine this assumption, we selected to trackthe anticonvulsant carbamazepine in a real WWTP effluent sample, alongside other
occurring pharmaceuticals as the ones analyzed in the extended experiment (Tab. 3.2).
Carbamazepine was chosen as a test case, as it was found in a high concentration
(1.29µg L−1) in the effluent.
Two different control experiments were conducted without nanoparticles and without
89
4. Results and discussionUV-irradiation for 45 minutes, to assure that only the combination of nanoparticles
and UV-radiation causes the degradation of the pharmaceuticals. Without nanoparti-
cles, no significant change in the monitored concentrations occurred. After irradiation,
the average change over the monitored drugs was 0.8% (SD 4.8%). However, for the
controls with nanoparticles kept in the dark, we observed an initial drop in the con-
centrations before they stabilized. This condition was reliably reached after the initial
30 minutes. Between the 30 minute mark and the end of the experiment 15 minutes
later the changes in concentration were 0.3% (SD 4.9%) for TiO2 and 0.2% (SD 5.7%)
for ZnO. The initial drop is due to the adsorption on the catalyst’s surface until the
adsorption-desorption equilibrium is reached. These results confirm the idea that the
UV-radiation per se does not induce the degradation process nor the nanoparticles
without UV-irradiation.
The concentration of carbamazepine was, however, considerably reduced over time in
the presence of the catalysts and UV-radiation. Similar behavior was observed for car-
bamazepine present in the wastewater effluent sample as for the ‘clean’ experiment.
In Fig. 4.10 the two experiments with carbamazepine on each of the two catalysts are
compared. It can be noticed that the degradation by ZnO is significantly faster than
with TiO2 in both setups, which is in high accordance with the conducted simulation
of the degradation. These results are shown in Tab. 4.2 and demonstrate that carba-
mazepine can adsorb more than 40 times faster on the ZnO than on the TiO2 surface.
Because of this, ZnO presents a higher degradation rate compared to TiO2 regardless
of its larger surface area.
Table 4.2.: Adsorption and desorption rate constants derived from the experiments
with carbamazepine using photocatalytic TiO2 and ZnO nanoparticles.
catalysts kads in m s−1 kdes in s−1TiO2 5.3 • 10−9 4.5 • 10−4
ZnO 2.2 • 10−7 5.9 • 10−3
When the parameters determined from the Millipore water experiment (Fig. 4.10 a, b)
are compared to the outcome from the effluent (Fig. 4.10 c, d) similar results can be
found. This similarity shows that the effluent background does not reduce the effi-
ciency of the selected photocatalytic particles, and the method to model the degrada-
tion in the Millipore water experiment can be applied for pharmaceuticals investigated
in the effluent as well.
90
4.4. Wastewater treatment plant effluent
020406080100
Degrad
ationra
tioC(t)
/C(0)(%
)
simulationexperiment
0 20 40 60020406080100
Time t (min)0 20 40 60
TiO2 ZnO
isolate
dC(0
)=12.0
mgL–1
effluen
tC(0
)=1.4µ
gL–1
a)
c)
b)
d)
Figure 4.10.: Measured concentration during the degradation of carbamazepine un-
der UV irradiation with 1.0 g L−1 catalysts TiO2 (a,c) and ZnO (b,d). In the
upper row, carbamazepine was dissolved in millipore water (a+b) and
measured by UV-vis spectrophotometry. In the lower row the results
of the degradation of carbamazepine in the treated effluent analysed by
HPLC-MS/MS-method are shown. The full lines represent fits for carba-
mazepine dissolved in millipore water according to the presented model
using the values of kads and kdes determined from experiments in the dark
(Tab. 4.2).
4.4.2. Degradation of pharmaceuticals in the effluent
The degradation results were traced for all target pharmaceuticals and are presented
in the Appendix - chapter B (p. 103). For the SPE extraction, a sample volume of 1mL
was necessary, which allowed a high temporal resolution monitoring with ten samples
throughout one hour. With the larger typical sample size, the experiment would have
been disturbed by taking out to much compared to the initial volume. An overview of
91
4. Results and discussionthe degradation curve based on the two photocatalytic materials is shown in Fig. 4.11.
After 40min, an average degradation of more than 95% for the samples treated with
ZnO was already observed. During the same period, the pharmaceuticals treated with
TiO2 degraded by 40%.
0 10 20 30 40 50 600
20
40
60
80
100
Time t (min)
Degradationratio
C(t)/C(0)(%)
deviationTiO2ZnO
Figure 4.11.: Average degradation ratio over time of the 14 selected pharmaceuticals
(Tab. 3.2) measured by HPLC-MS/MS-method. The grey area corresponds
to the standard deviation.
The simulation shows that treatment with TiO2 would take over four hours to achieve
the same result as ZnO. These differences in degradation rates are even more sig-
nificant, taking into account the smaller surface area of ZnO. The resulting apparent
rate constants and adsorption rate constants are listed in Tab. 4.3 and following the
results from carbamazepine dissolved in Millipore water. In the literature, a variety of
new approaches besides commercial nanoparticles are presented. The apparent rate
constants found, for example from TiO2 nanowires is on average, the same order of
magnitude as the commercial TiO2 particles, but slower compared to the ZnO particles
[183].
Furthermore, a lower selectivity of ZnO compared to TiO2 was observed. In the ZnO
experiments, all selected pharmaceuticals are degraded similarly with just slight devia-
92
4.4. Wastewater treatment plant effluent
Table 4.3.: Apparent rate constants average and adsorption rate constants average for
the 14 studied pharmaceuticals (Tab. 3.2) with the photocatalysts TiO2 and
ZnO.
catalysts kapp in s−1 kads in m s−1
TiO2 1.4 • 10−2 4.0 • 10−9
ZnO 8.6 • 10−2 2.7 • 10−7
tions. This characteristic is significant for applications due to the different mixtures of
pharmaceuticals present in wastewater depending on regional consumption patterns
or seasonal fluctuations. Treating pharmaceuticals present in WWTP effluents using
ZnO and UV-radiation will result in a near-complete degradation of the pollutants in a
relatively short period.
93
5. Conclusions
The simultaneous increase in the worldwide population and living standards in com-
bination with progressive climate change lead to a desperate need for more clean
water. Appropriate technologies for water reuse are an essential part of coping with
this global social challenge. The direct use of treated municipal wastewater for irriga-
tion of agricultural land is at the moment hindered by the presence of organic trace
substances, like pharmaceuticals. When irrigating fertile land, these trace substances
accumulate and subsequently damage soil organisms or are absorbed by plants and
get back into our food chain. Similarly, industrial production processes generate by-
products such as dyes, biocides, and other inert compounds that get into municipal
wastewater or directly into waterways. In contrast to municipal wastewater treatment,
the industrial application is not focused on removing a multitude of low-concentration
substances, but rather the elimination of a few concentrated problematic organic con-
taminants. Photocatalytic degradation is a technology that can potentially resolve
these kinds of challenges. A general model describing the photocatalytic degradation
process is needed to evaluate the performance of differentmaterial combinations and
setups objectively, helping with identification of patterns and optimization pathways.
The creation and evaluation of such a model was the focus of this thesis.
The first set of experiments discussed in this thesis helped to establish the funda-
mental interactions in the model. Through iterations between the model creation
and experimental design, a best-practice setup was implemented to examine the ad-
sorption/desorption equilibrium efficiently. The combination of the model and experi-
ments showed that our setup was limited by the adsorption rate of the test substances
on the catalytic surfaces. By reducing the applied UV-irradiation, we showed that for
the combination of TiO2 and methylene blue, the reaction rate and the adsorption
rate were actually in close approximation to each other. Would these experiments
95
5. Conclusionsonly studied by the common usage of an apparent exponential rate constant, this con-
nection could not be made.
After the general model was established, WWTP effluent was used to evaluate the
model. Compared to the clean experiments carried out to this point, the matrix of
the effluent presents a significant challenge. It was shown that the background did
not hinder the performance of the model, as long as the overall organic load is rea-
sonably low, as to be expected after the ordinary processing steps. The tracked va-
riety of pharmaceuticals could be treated as disconnected cases. As collecting the
adsorption-desorption characteristics of all investigated molecules was not possible
in a reasonable amount of time, the model was used to analyze the complete set as
a virtual average molecule, to compare the performance of the used photocatalytic
material.
A few samples were analyzed using NPOC locally, evaluating the multi-species part
of the model. A systematic investigation of the organic carbon development during
the degradation experiments was not possible in our setup, through the needed sam-
ple size for each measurement point. Therefore, the model was tested successfully
against published data.
Upon entering the thematic field of photocatalytic degradation, it became clear, that
most publications evaluated their experimental results with an exponential fitted ap-
parent rate constant. While this can enable comparison between closely related ex-
periments, it makes it difficult and sometimes even impossible to compare results
between publications. This was one of the reasons to design a model that incorpo-
rates essential parameters describing the experimental system, like the available cat-
alytic surface area, or the approximately area a molecule can cover. Including the
adsorption-desorption dynamics in the model, enables the model to approximate
edge cases, like the linear degradation in the case of high pollutant concentrations.
It allows the estimations of the catalytic surface coverage by the molecules. Besides,
aiding in the evaluation of typical degradation experiments, the multi-species exten-
sion of the model helps to investigate the TOC within the same theoretical framework.
This connects the typically separated experiments and enables a more meaningful in-
vestigation of photocatalytic systems.
While it was tempting to expand the model with more parameters, or a more realistic
reaction network, it is essential to realize that most of these parameters would not be
accessible by experiments. In the end, an over-detailed model would fold back into a
96
system with very similar characteristics to the proposed model, as unknown parame-
ters would need to be merged again. Overall the model is designed to be integrated
into an experimental workflow. To aid the adoption of the model, the incorporation
into existing processes needs to be possible without great hurdles. This was the mo-
tivation to make a ready-to-use implementation of this work available. Providing a
flexible infrastructure facilitates potential extensions to the model, to cover specific
scenarios. For example, multiple target molecules can be simulated at once. Model-
ing a flow reactor-like setup if feasible using an additional reservoir with kreac = 0 and
connect it with fluxes describing the exchange to the reaction reservoir. Moreover,
alterations of the presented models are possible; for example, the alteration of the
target priority of the excess bonds.
While the essential usability of the photocatalytic pathway to remove leftover organic
matter after the conventional wastewater treatment, is well-established in literature
and shown in this work, a quick introduction into the routine treatment process is
unlikely. The biggest hurdles are engineering challenges and the missing knowledge
over the ecological impact of a large scale deployment.
For example, in the WWTP in Dresden-Kaditz a new treatment facility that processes
the water for just 60min would need a water capacity of ≈ 90000 L. In this order
of magnitude, the illumination of the overall system is extremely challenging, as the
UV-light can pass a couple of centimeters through a nanocatalyst solution before it is
mostly absorbed. This problem can be mitigated with the use of a light-guiding sys-
tem made from quartz glass fibers or sheets. Immobilization can be used to avoid
the complex process of separating nanoparticles from a constant water flow. While it
helps to reduce the amount of catalyst material reaching the environment, it severely
reduces the available surface area at the same time. This reduction leads to longer re-
tention times and therefore, an even larger footprint of the potential treatment facility.
Therefore, finding the best catalyst to cut down on the processing time is imperative.
These up-scaling problems can be solved, but they hinder the adoption of this technol-
ogy, especially while other approaches are already successfully employed for the same
task. However, photocatalytic degradation can be an attractive solution, as it is more
energy-efficient than ozone treatment and produces less waste compared to active-
carbon filtration. The most promising path forward towards a large scale application
is probably the synergetic combination with an ozone treatment setup.
While a few challenges remain to be solved, the presentedmodel can help to overcome
97
5. Conclusionsthem. It can assist with the screening of various materials in different configurations
for the use in wastewater treatment setups. By providing comparable results, complex
setups can be optimized in a meaning full way. All in all photocatalytic degradation
should play an important role in a refined wastewater treatment process, and the
presented model can support this effort.
98
Appendix
A. Analytical solution
Solving the system of ordinary differential equations (Eqs. 3.9, 3.10 , p. 58) describing
the single molecule model. This solution is limited to small surface coverage Θ � 1.
The full solution is also presented in Eq. 3.15 and Eq. 3.16 (p. 60).
Most features of pdom can be accessed directly from its command-line tools. The easiest way to install them onyour system is via pipx. pipx is a packagemenager for tools written in python that helps to keep them isolated andup to date. Some notes on how to get pipx running can be found at the end of this section. If you just need theCLI, use the following line to install pdom.
$ pipx install pdom
1.2 Library
You can also install the pdom library directly through the Python Package Index (PyPI) for use in your ownprojects. The use of a virtual environment is recommended.
$ pip install pdom
If the stable version of pdom on PyPI is missing a particular function, you can install the latest developmentversion directly from the GitHub repository.
To work with the source code clone the repository from GitHub and install the requirements. The source code isaccompanied by the documentation and an extensive collection of test cases.
Python is not installed by default under Windows. You can get the installer from the Python download page. Thepython package system pip is already included in the latest releases.
In the windows commandline pipx can then be installed.
See also the source code documentation of pdom.Simulate.
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3 Configuration
3.1 Simulation
To run the simulation pdom needs a couple of information from the user. For pdom, this data is saved in an .inifile. This ensures that the results of a simulation can always be accompanied by the parameters that created them.
A simple config for pdom looks like this:
Listing 1: simple.ini
[SIMULATION]id = simple_degradation_methylene_bluemulti = Falsefit = Falseduration = 5 h
The parameters are arranged in different sections. Not all sections need to exist for each simulation.
To create a new .ini file you can use the configuration tool of pdom.
$ pdom.config --out 'my_new.ini'
It will guide you through the process by collecting all relevant information. For the parameters of the initialmolecule, it is helpful to look up its chemID in PubChem before you start the process. This enables the automaticgathering of the molecule parameters from this database.
Most of the time, the automatic process should suffice. But if you want to build your .ini file from scratch, takea look into the available Configuration settings.
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3.2 Experimental data
To extract parameters, we need to compare experimental data to the simulation. This data needs to be providedin a structured way. For pdom we use a .json file. Depending on the type of fit you want to carry out, theavailable features differ slightly.
Adsorption-Desorption experiments
Adsorption-Desorption experiments in the dark are analyzed with the single-species model. As it is common tohave multiple repetitions that are based on the same setup. pdom supports multiple time series in its fits. Theinitial concentration and time steps can be different between the series. Below are examples of such a data file.
For degradation experiments all time series have to start with the same initial concentration set in the .ini file.This is the data file from the example Degradation fit.
To compare multi-species model simulations to experiments, TOC (or NPOC) can be used. In general, the fit toTOC data is the last step in the experiment analytics. This fit is limited to a single TOC curve, due to the usuallydemanding experimental process. If multiple TOC experiments are available, the results should be average beforesimulation. As just one initial concentration is needed, it is taken from the .ini file.
units molecule/m^3, molecule/L, mol/m^3, mmol/L, M, mol/L, mo/mc, g/L,mg/L, g/m^3
• concentration_surface → float
default 0
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units molecule/m^2, mol/m^2, g/m^2, mg/m^2
note if concentration_surface is not set system is considered in equilibrium (dark)
• k_ads → float
default 1E-9 m/s
unit m/s
• k_des → float
default 1E-3 1/s
unit 1/s
• k_reac → float
default 1E-2 1/s
unit 1/s
FIT
This section is just active if fit is True
• type → str
default dark
note dark, reaction or toc
• search → str
default relative
note minima search absolute, relative or relative_square
note does not apply to fit type toc
• max_step → int
default 100
note does not apply to fit type toc
MULTI
This section is just active if multi is True
• split_model → str
default fragmentation
note incremental, fragmentation or excess_bonds
• desorption_model → str
default weak
note weak or strong
• TOC_estimation → str
default all
note all or volume
• segment_export → str
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default mass
note mass or molecule_count
MULTI_WEAK
This section is just active if desorption_model is set to weak. Just one value needed if k_des isset.
• beta_0 → float
default -0.029 1/s
unit 1/s
• beta_1 → float
default 0.8 1/s
unit 1/s
MULTI_STRONG
This section is just active if desorption_model is set to strong
• E_0 → float
default 44.0 kJ/mol
unit kJ/mol
• E_1 → float
default 3.0 kJ/mol
unit kJ/mol
• alpha_0 → float
default 1.51e8 1/s
unit 1/s
• alpha_1 → float
default 0.412
4 Examples
4.1 Adsorption - Desorption equilibrium
In this first example, the goal is to simulate a system reaching equilibrium in the dark. To run the simulation, weare going to create a configuration file for pdom first. After calling pdom.config we need to answer a fewquestions. The parts which require user input are highlighted in grey.
$ pdom.configID of the system (avoid spaces): example_ads_des
Should data be fitted to the simulation?1: fit2: just simulation
(continues on next page)
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(continued from previous page)
Your choice: 2
What kind of simulation?1: Adsorption-Desorption2: Degradation3: TOC
Your choice: 1
How can you identify the initial molecule?1: chemID (https://pubchem.ncbi.nlm.nih.gov)2: name
Your choice: 1Molecule: 2764Found ciprofloxacin (C17H18FN3O3)
What is the catalyst concentration?the allowed unis are: g/m^3, g/L, mg/L
Value: 1 g/L
What is the catalyst surface area?the allowed unis are: m^2/g, cm^2/g
Value: 56 m^2/g
What is the overall volume?the allowed unis are: m^3, L, cm^3, mL
Value: 0.3 L
How long should the simulation be?the allowed unis are: h, min, s
Value: 15 min
What is the adsorption constant?the allowed unis are: m/s
Value: 3.7E-8 m/s
What is the desorption constant?the allowed unis are: 1/s
Value: 2.0E-2 1/s
What is concentration in the solution?the allowed unis are: molecule/m^3, molecule/L, mol/m^3, mmol/L, M, mol/L, mo/
→˓mc, g/L, mg/L, g/m^3Value: 0.1 mmol/L
What is concentration on the surface?the allowed unis are: molecule/m^2, mol/m^2, g/m^2, mg/m^2
Value: 0 mol/m^2
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The resulting file example_ads_des.ini is now in your working directory. To start the simulation simplycall pdom:
$ pdom example_ads_des.iniStart calculating single species modelCalculation finished!Results saved in <your_working_dir>/example_ads_des
In the newly created folder <your_working_dir>/example_ads_des, you find the raw data files withcorresponding units and a plot of the concentration development over time.
0 2 4 6 8 10 12 14time t (min)
0
5
10
15
20
25
30
volu
me
conc
entr
atio
n C
(g/m
3 )
0
10
20
30
40
50
surf
ace
conc
entr
atio
n C
(g/
m2 )
Fig. 1: Development of the concentration in solution and on the surface during the equilibration in the dark.
4.2 Degradation fit
Using the single species model, we fit in this example the reaction constant 𝑘reac to experimental data. Withpdom.config we can create example_reac_fit.ini. The parts which require user input are highlightedin grey.
$ pdom.configID of the system (avoid spaces): example_reac_fit
Should data be fitted to the simulation?1: fit2: just simulation
Your choice: 1
What kind of experiment was conducted?(continues on next page)
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(continued from previous page)
1: Adsorption-Desorption2: Degradation3: TOC
Your choice: 2
How can you identify the initial molecule?1: chemID (https://pubchem.ncbi.nlm.nih.gov)2: name
Your choice: 1Molecule: 2764Found ciprofloxacin (C17H18FN3O3)
What is the catalyst concentration?the allowed unis are: g/m^3, g/L, mg/L
Value: 1.0 g/L
What is the catalyst surface area?the allowed unis are: m^2/g, cm^2/g
Value: 56 m^2/g
What is the overall volume?the allowed unis are: m^3, L, cm^3, mL
Value: 1 L
How long should the simulation be?the allowed unis are: h, min, s
Value: 0.8 h
Which constant is known?1: k_ads2: k_des
Your choice: 1
What is the adsorption constant?the allowed unis are: m/s
Value: 3.7E-8 m/s
What is concentration in the solution?the allowed unis are: molecule/m^3, molecule/L, mol/m^3, mmol/L, M, mol/L, mo/
→˓mc, g/L, mg/L, g/m^3Value: 3.8 mg/L
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The resulting file example_reac_fit.ini is now in your working directory. Next, the experimental dataneeds to be stored as example_reac_fit.json. In this example, two time series with the same initialconcentrations are used.
In the same folder, you find the raw data files with corresponding units. The saved plot shows the concentrationdevelopment over time compared to the experimental results.
4.3 TOC simulation
Fragmentation
When the overall degradation of an organic molecule should be simulated, one of the multi-species models mustbe used. Three different split models are available in pdom:
• incremental
• fragmentation
• excess bonds
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To model the generalized split species, the size dependents of the desorption constant 𝑘ads must be described. Youcan either choose strong or weak dependents for your simulation. We chose weak dependents in this example,due to the fewer needed parameters.
As before the config file example_toc_sim.ini can be generated with pdom.config. Lines with requireuser input are highlighted in grey.
$ pdom.configID of the system (avoid spaces): example_toc_sim
Should data be fitted to the simulation?1: fit2: just simulation
Your choice: 2
What kind of simulation?1: Adsorption-Desorption2: Degradation3: TOC
Your choice: 3
How can you identify the initial molecule?1: chemID (https://pubchem.ncbi.nlm.nih.gov)2: name
Your choice: 1Molecule: 4139Found methylene blue cation (C16H18N3S+)
What is the catalyst concentration?the allowed unis are: g/m^3, g/L, mg/L
Value: 1 g/L
What is the catalyst surface area?the allowed unis are: m^2/g, cm^2/g
Value: 56 m^2/g
What is the overall volume?the allowed unis are: m^3, L, cm^3, mL
Value: 0.4 L
How long should the simulation be?the allowed unis are: h, min, s
Value: 4 h
Which split model should be used?1: incremental2: fragmentation3: excess_bonds (slow)
Your choice: 2
Is the system in equilibrium (dark)?1: Yes2: No
Your choice: 1
(continues on next page)
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(continued from previous page)
Which model should be usedfor the estimation of size dependent k_des?
1: Strong2: Weak
Your choice: 2
What is the adsorption constant?the allowed unis are: m/s
Value: 2.1E-8 m/s
What is the desorption constant?the allowed unis are: 1/s
Value: 2.85E-2 1/s
What is the reaction constant?the allowed unis are: 1/s
Value: 2.85E-1 1/s
What is the value of beta_1?the allowed unis are: 1/s
Value: 0.2 1/s
What is concentration in the solution?the allowed unis are: molecule/m^3, molecule/L, mol/m^3, mmol/L, M, mol/L, mo/
→˓mc, g/L, mg/L, g/m^3Value: 4 mg/L
With the generated config example_toc_sim.ini we can start the simulation with pdom.
$ pdom example_toc_sim.iniStart calculating multi species modelCalculation finished!Results saved in <your_working_dir>/example_toc_sim
In the folder <your_working_dir>/example_toc_sim, you find the raw data files with correspondingunits and three plots. The first plot is an overview with TOC and the concentration of the initial molecule insolution. The other two show concentration developments of the segments in solution and on the surface.
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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0time t (h)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
volu
me
conc
entr
atio
n C
(g/m
3 )
0.0
0.5
1.0
1.5
2.0
2.5
TOC C
(g/m
3 )
Fig. 3: Development of the concentration in solution and the total organic carbon (TOC) using the fragmentationsplit model.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0time t (h)
10 6
10 5
10 4
10 3
10 2
10 1
volu
me
conc
entr
atio
n C
(g/m
3 )
2
4
6
8
10
12
14
carb
on c
ount
Fig. 4: Development of the segments in solution when using the fragmentation split model.
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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0time t (h)
10 8
10 7
10 6
10 5
10 4
10 3
10 2
10 1
surf
ace
conc
entr
atio
n C
(g/
m2 )
2
4
6
8
10
12
14
carb
on c
ount
Fig. 5: Development of the segments on the surface when using the fragmentation split model.
Incremental
Because pdom is based on configuration files, you can simply make a copy of example_toc_sim.ini andchange the settings quickly for a new simulation. You can alter the split_model key in the section MULTI toincremental for example:
In the same folder, you find the raw data files with corresponding units. The saved plot shows the TOC devel-opment over time compared to the experimental results.
0 1 2 3 4 5 6time t (h)
0
2
4
6
8
10
12
TOC
(g/m
3 )
simulationexperiment
Fig. 9: Experimental TOC measurements compared with the simulation results.
5 Source documentation
5.1 pdom.Simulate
class pdom.Simulate(config_file, out_folder=None, data_file=None, overwrites=None, resolu-tion=250)
Class to simulation different degradation models
Parameters
• config_file (str, Path) – .ini file to load
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• out_folder (str, Path, optional) – folder to save the results
Diffusion constant in air depending on molar volume and weight Based on the FSG model with con-stants from the Handbook of chemical property estimation methods.
standard_atomic_weight = {'Ac': 225.027, 'Ag': 107.87, ...}Mapping element symbol to standard corresponding atomic weight.
Source “Atomic weights of the elements 2013” (IUPAC) [MCB+16]
Returns standard atomic weight [u]
Return type dict
classmethod unit_convert(value, unit)Convert into pdom base units
Note Base units are s, 1/s, m, m/s, W/m^2, K, g/m^3, m^2/g, m^3, cm^3/mol, m^2/molecule, kJ/mol
Parameters
• value (float, int) –
• unit (str) –
Returns converted value
Return type float
unit_convert_concentration(value, unit, cfg=None)Concentration to number of molecules
Note A simulation config can be passed, to use alternative parameters, for example to con-vert TOC.
Parameters
• value (float, int) – value
• unit (str) – unit
• cfg (dict, optional) – simulation config
Returns 𝑁 - number of molecules [1]
Return type float
static update_multi_k(config)Update the config for multi species models
This needs to be called after a basic setting is changed in the config, to update parameters dependingon species size.
Parameters config (dict) – simulation config
Returns simulation config
Return type dict
van_der_waals_radii = {'Ac': 2.0, 'Ag': 1.72, 'Al': 2.0, ...}Mapping element symbol to corresponding Van der Waals radius.
Note Radii that are not available in either of the sources have RvdW = 2.00.
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Source “van der Waals Volumes and Radii” by Bondi (1964) [Bon64], the value for H istaken from Rowland & Taylor (1996) [RT96]
Returns Van der Waals radii [Ang]
Return type dict
viscosity_water = <scipy.interpolate.interpolate.interp1d object>A smooth interpolation from 274 to 363 Kelvin. Viscosity is retuned in mPa*s | centipoise |(mN/m^2)*s.
Source Wikibooks - Stoffdaten Wasser
5.3 pdom.Molecule
class pdom.Molecule(identifier, properties, save=True)This class should not be initialised directly. Use one of the following class methods in-stead: from_chem_id(), from_folder(), from_inchi(), from_inchi_key(),from_iupac_name(), from_name()
Parameters
• identifier (dict) –
– name common name
– iupac_name IUPAC name (can be the same as common name)
– chem_id compound ID from PubChem
– inchi IUPAC International Chemical Identifier (human readable)
– inchi_key IUPAC International Chemical Identifier (hash)
• properties (dict) –
– chem_formula chemical formula e.g. ‘C10H22’
– chem_formdic chemical formula as dict
– mol_weight molecular weight in g/mol
– mol_volume molecular volume in cm^3/mol
– mol_surface largest projected surface area m^2/molecule
– excess_bonds number of bonds in excess of a simple carbon chain
– structure_3d atom position list
• save (bool) – save data tu the user cache
classmethod from_chem_id(chem_id, name=None, inchi_key=None)Create Molecule instance identified by a chemID from PubChem data.
Note if molecule is cached in Molecule.db_folder load from there
Parameters
• chem_id (int) – compound ID from PubChem
• name (str, optional) – overwrite compound name
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• inchi_key (str, optional) – IUPAC International Chemical Identifier (tocheck cache quickly)
Returns Molecule instance
classmethod from_folder(folder)create Molecule instance from a folder created by save
Parameters folder (str, folder) – molecule folder
Returns Molecule instance
classmethod from_name(name)Create Molecule instance identified by a name if unique
Note queries chem_id and calls from_chem_id()
Parameters name (str) – unique compound name
Returns Molecule instance
identifierdict of identifiers as described in Molecule
propertiesdict of properties as described in Molecule
save(folder=None, name=None)saves the molecule information to disk, can be loaded with from_folder()
Note If called without parameters the molecule is saved in an appropriate cache folderMolecule.db_folder.
Parameters
• folder (str, Path) – parent folder
• name (str) – molecule folder name (default INCHI key)
structure_3d(rotated=True)Returned 3d structure of the molecule
Parameters rotated (bool) – if True the structure is rotated to cover the maximumsurface in the xy space
Returns 3D structure (symbol, x, y, z)
Return type list
5.4 pdom.export
Helper functions to export simulation results.
pdom.export.fit_dark(cfg, result, result_raw)Export function for fit: Adsorption - Desorption experiment in the dark.
Parameters
• cfg (dict) – simulation config
• result (tuple) – fit_t, fit_y, k_ads, k_des
• result_raw – raw fit function result
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Result
• plot with fit and initial data points fit_dark.pdf
• space separated data file containing the fit fit_dark-values_calculated.txt
• space separated data file containing initial data pointsfit_dark-values_experiment.txt
• .json with the fitted parameters fit_dark.json
• .txt files with corresponding units (LaTeX formatted)
pdom.export.fit_single(cfg, result, result_raw)Export function for fit: single species degradation model.
Parameters
• cfg (dict) – simulation config
• result (tuple) – fit_t, fit_y, k_ads, k_des, k_reac
• result_raw – raw fit function result
Result
• plot with fit and initial data points fit_single.pdf
• space separated data file containing the fit fit_single-values_calculated.txt
• space separated data file containing initial data pointsfit_single-values_experiment.txt
• .json with the fitted parameters fit_single.json
• .txt files with corresponding units (LaTeX formatted)
pdom.export.fit_toc(cfg, sd_error, t, fit)Export function for fit: TOC.
Parameters
• cfg (dict) – simulation config
• sd_error (float) – standard derivation error
• t (ndarray) – fit time series
• fit (ndarray) – fit toc series
Result
• plot with fit and initial data points | fit_toc.pdf
• space separated data file containing the fit | fit_toc-values_calculated.txt
• space separated data file containing initial data points |fit_toc-values_experiment.txt
• .json with the fitted parameters | fit_toc.json
• .txt files with corresponding units (LaTeX formatted)
pdom.export.multi_species(cfg, t, N_surf, N_vol)Export function for incremental and fragmentation multi species model simulations.
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Parameters
• cfg (dict) – simulation config
• t (ndarray) – fit time series
• N_surf (ndarray) – number of molecules on the surface
• N_vol (ndarray) – number of molecules in solution
Result
• plot with concentration development in solution and TOC c_volume-toc.pdf
• plot of the segments in solution and on the surface volume_segments.pdf,solution_segments.pdf
• space separated data file containing the concentrations in solutionmulti_species-values_volume.txt
• space separated data file containing the concentrations on the surfacemulti_species-values_surface.txt
• .txt files with corresponding units (LaTeX formatted)
pdom.export.multi_species_bonds(cfg, t, N_surf_detail, N_vol_detail)Export function for incremental and fragmentation multi species model simulations.
Parameters
• cfg (dict) – simulation config
• t (ndarray) – fit time series
• N_surf_detail (ndarray) – number of molecules on the surface
• N_vol_detail (ndarray) – number of molecules in solution
Result
• same files as multi_species()
• plot of the average excess bond count excess_bonds.pdf
• space separated data file containing the average number of excess bondsmulti_species-excess_bonds
pdom.export.single_species(cfg, t, N_surf, N_vol)Export function single species model simulations.
Parameters
• cfg (dict) – simulation config
• t (ndarray) – fit time series
• N_surf (ndarray) – number of molecules on the surface
• N_vol (ndarray) – number of molecules in solution
Result
• plot with concentration development in solution and on the surfacesingle_species.pdf
• space separated data file containing the concentrations in solutionsingle_species-values_volume.txt
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• space separated data file containing the concentrations on the surfacesingle_species-values_surface.txt
• .txt files with corresponding units (LaTeX formatted)
References
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[RT96] R. Scott Rowland and Robin Taylor. Intermolecular Nonbonded Contact Distances in Organic Crys-tal Structures: Comparison with Distances Expected from van der Waals Radii. Journal of PhysicalChemistry, 100(18):7384–7391, 1996. doi:10.1021/jp953141+.
[TN82] William A. Tucker and Leslie H. Nelken. Diffusion Coefficients in Air and Water. In Warren J.Lyman, William F. Reehl, and David H. Rosenblatt, editors, Handbook of chemical property es-timation methods : environmental behavior of organic compounds. McGraw-Hill, 1982. URL:https://archive.org/details/handbookofchemic0000lyma.
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List of figures
2.1. Relationship between the model and the real and virtual systems. . . . . 21
2.2. Energy diagram for a typical n-type semiconductor. . . . . . . . . . . . . 24
2.3. Band structure of the anatase and rutile phase of TiO2. . . . . . . . . . . 25
2.4. Energy diagram for a typical n-type semiconductor in contact with an
electrolyte in dark and under illumination. . . . . . . . . . . . . . . . . . . 28
2.5. Bandgap energies and absorption edges for selected metal oxides. . . . 32
2.6. Bandgap energies and absorption edges for selected chalcogenides and
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Oliveira, and G. de Aragão Umbuzeiro.
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dyes and pigments. 3rd ed. Weinheim: Wiley-VCH, 2003.
[53] M. Levitt and A. Warshel. “Computer simulation of protein folding”.
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